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| ARCHITECTVRA
K MILI T.ARIS.
A B C 1 1 1 4.
1 '
the
1. DeDelineationibus.
1. DeOrthographia & ichnographia.
The Stereometria 1 & Sketch.
4a mechanical means ©> and the Offenfione;
effort
Nicholas Goldmann
Vratiflavicnfis Silefii;
SAN FERNANDO
Lvcd. Batavor.
Officina Elfeviriana.
Jae give xinu
500 E A T 1 500 1 100 C.
am a perennial ^ & cultoresfcientia by INO-loving Defenfe whole univerfum spheres. Hadienus delay report to the great rhythm-and qttotidie wondering are they aliqttos to be a celebrity sua grabs: Cult so generously given greater verb "to no more than three ifwere Curitim Ali Salem it a
lllipilluftrem JjlcndoremTuum, Cast-matter of their recommendations agree dibits desire, the more there is, for the labors of the disciples in a way worthy afimari experiun-tur, go back, Scientejudicium a view to the all of proficif-; aliasfape ^ important inf.ni both the buy-dusiriam viltprecio to go on learning; efur expertantur those who hutcfoliinfli-safe deferviunt Me & excellent etfi greater by a little more endurable propofttafintstamen hocfudiu arrifit great pleasure to which the amp sim um He departed's a domef po-ish crowd impctrare's, plus the time and laborispo co-ownership, which is that the special-Mthi the premises. Ned, verily, I from in inf nit a expanfone, cuivisparti fctentia me, I applied, but to him, it especially, and of which the Profeftoni men cjfet-commodatifima. For, in the out of the Republics of war, we should not be infimagio-ri quaritur- verfdnti, in this kind of the palm of
Archbishopricks
Dedication.
Architecture Nofrius entitled to the same educational experience fumy fumfi. One man hath no trouble quadrienntiim be spent on; And that it would continue to shed the firm with a finger-f er, teaching munusfife epi, in aiming at the mouth of it, it should have some gram-third favorably. Haque Nobihfimorum of certain highly-dam assistant, whose names were not silent time, the boards, nonfolum'Delmeationum that er at the news, but also Ichnographica and stereometricorum as that info text nm, fupputavi. When autemmulta the hocgenerefcripta prodie-crisis fmtqtie into the hands irnpofti-bile 'fuperat will be the same, even the wicked men, clapped his inquiry. The labor-priosverb Laudibm's cnmulare dedecor i ef necfides those eulogies given. So-quefolum wrong force ntproponam what is exifimem-resolved invention, what nu ? ey- in mind. Four d 'verbpratrip us revocariillapoterunt heads. The bodies of Warnecombe ef, then the Ionians and that they are in all of us of the first hbrifefenfonem Delinea-t of the vibrating string is, to the majtufpatium, which ipfusfemifis effcliciter, utpatet, when I stretch. T on
Dedication.
Lower storage place that Ichnogra-jeered by tabulisftipputatis, orthographus-phy nemp'e noftra retained compendtose (b swiftly on paper than on the field abftol-vamus. 1 duel verb repeat that [blidi floor-tat is not already praceptisfted ( ft board, accuratifiime shown. the last, not last place of putting it is that the irregular IBM inquibusfigura retain eftftaci-mud (ftexpeditiftimum the mech-codification imagined. and since the beginning Seculin off rl circumfpicerem, llluftri your name, the opufiulum and pracipueLati ? whether model jnfcribi be judges, the force that all gather mecenfuramtanti beginning volentcmfubiijfte: £ juemyft, meapro-barifenfero is, you have to detre-ciatores eritftitiftacium. Today Se fitften-tat n} llluftrifitmo to thy humble me prof purchase, (ft happy Rerumfucccjftum their recommendations ardentibns malice.
New Batavortim calcndis March Anntei <.!:> Jg world.
Nicholas Goldman.
The op R O OE 1000 1 5 M.
THEY
"Rbivm azdificatio, if Prill its main origin fpefte-mouse, there is fresh or n?per was found, but the world's foremost juventaufurpata. The inventor, who beheaded his victim and then contratftus confcientise anger pr?mum masnibusmancipavit, iacramo-nimentum teftantur Caine. Corihujus earnest yet-to-autorede such acquisition; Merc ?ss?tur be surprised that the wicked and nefarious also are some of the race-fuoprofue crisis. In this way the behavior of a good from evil; ortx laws are: fic governments from the wicked vaft-toreNimrodo more the blood, the height-direction; juftitia governments and ramen and pre-settlement fuffulta proprerea are examined, the divine omnipotence by-durable. The first human race-free rate for any terror are widely *
* 4 brash-
The OE m i v m.
brás abftrufit, finished fcelens Furia, an xium Meru mind-to-ialutem of the flooring inftigarunt, except no fear of being beaten by the fault profcaturit. Yet it is undoubtedly await Xdi-ery small moment! was utprimordia works under afl'olent shot. And then think about Architecture-fated military ccepifle-mouse; for when the Wars of the unknown efl'env, the military will not be able to be conceived, not in what: from the illaderivantur. Pollquam Verde-bit, which fluftusaliquo at the ABF-conderant face again renewed the art of human adinvenifl'e, the demon-ftra, which are immediately fecutus wars, & prisoners. And so, when the field of plant-ruinous? Quabilis and fertility, fertilizing reperifl'ent towers velarcem rather, with the city of fuperbiflima set up, which is just fedes Empire and firmiflimum ejuf-protection was the same. Indeed, the first Arcbitefturx military, which is called STRENGTHENING-nu exotic language, culture fuifl'e proclaimed upright. Auftahincfuitfcientiaaflidui-Tate feralium Asia by war-tainted pience.
pientes. For when you were the lands of the empire from the Aftyriis Babyloniifque from being stolen, they are from Perils Medifque dcjedti; hofque again Graci perdomuerunc, the arms of the Romans, who were at last, is the casting one's liberty and the judgment of the government from allowing itself to be out of my way knowing that these things; in fpoliare funt.Ex tiasj go astray-that is to say, iifdem Quarters, Where the Sun, Holy Bible gives rise to. Such as the habit the earth, for the first time? To age, fuiffe, atqueex The other colonies of soldiers in the world, difperfas efle, nemoambigit. There Herodotus mo-nimentade walls Babylon VA-ftomiraculo: The Achmetha with the I-dos, the heights of the towers and a wall-run, facri lend continentur- overcame their earlier Greekes fagacitas that there folumurbes munivcrunt, but also sional one of the mountains, and Ifthmum ipfum castles and barrier concluferunt - caftra that imofuavallo fcpferunt; by whom the post-Roman vidlt of Macedonia :, order mutuarunt. Hipofteriores at the fact that penetratunt ur-to-defenfionem a la teribusexoptarent Anger luliusimpera-
Y tortorThapfum city, castris snake inflection drag conduct, nor ludxos this mode lives which, graviffimus author greed Claudius-run season, the right to defense emifte it; and he adds, that to oblige, by means of art-which effecifl'e the walls, so that the sides of the aflalientium to the iftum patefeerent. Parentumenoftro-run Aita were treated to a random incident-dit>, all of which were found vetepum> one as i • However alterurrum Weteakyrs is predominant, in himself and by that be made confuevit denominate their chief characteristic. Other counts is divifio fcientix which Architethiram this geometry or mechanical. Geometric that will be covered, which are the foundations of mathematics learning; much of Trigonome-country, it can serve certainty produced, mechanics, which, prior principles inha, seeking, fcrupulofas ratios so-Gligo and the celeritateinventionum & conftru & ionum foll I quickly than .Porro neceffaria So far less trade-execution causes longer. For who is there in the whole world developed a he does not know, who is Creator of all, is made of works munitum? all shall speak his efle ArchitcCtum, to whom all from the experts in the art of war-lui Engineering had vocabu
tix only, & as much as the strength of the bodies of the armed men, inferviat. This haudine su?pte defcriberes a good mu-nicndi expert. Vertim await a final verdict, not everyone is suited to Defcriptio, for it is the ability of using hands, those artists fublimis they need. It completed the first artist to necefiaria elle Geo-meter, at the end of the eftedorum ftabilis foundation, will never yield. Hence, the arithmetical triangle count that? feientiam special occupied the ex-peditusfit. Im-not an expert, and the graphic is done pidturse. CCR-art Proipeftivx us, -indignum Fane seemed to be spread by Artifice, Profpedtum future work 1m-subjugated fue poftulanti not show pofle. Architedura the civil-jungendaeft because Gates smartly-mints, Microsoft penfilium imped?menta from this book, and I cohzrenri-chanica inventions are equal. Caufie natural objects and the world diverfitatem dijudicabunt and water aerifque f?s lubritas here cxplorari poteric. Hifto-riarumm impofuerunt, quodingeniomilitia;
P U O OE 1000 1 5 M.
carages & Obfidionum evolution, especially ocular perluftratio, IP-Fi huge honor conciliabit; For the exploitation of another case fuum can avoid peri-tub was so, later on in the war, with the twice-a matter of no man sin, may be appointed. Philo-fophiipfum inftruent properties virtues, not greedy or a tia or morofitate strike; or ts-occupying crudeliratem, with juftitia-culcata, foveadam purer. Demon-ftrationum verb building, faftigium work is imposed - for con-cedcndum here, save solid foundation tis fubftruatur. To all these things, too, you campeftris must be linked to the practice of, fegn, for, immifla through the ears, anal-mum stirred by all that which I qujeoculari perluftratione confpicamur. The end of the verb of fortification, the only hiedatur, utfub fu-prema-the law of salus is made of listeners of the citizens & soldiers. So the best and gram-Vift quifque Defenfionem prxei-boys tend fumfit; and building a network that belongs here invifibi de-lis is bent on Mars and Vulcan, b quandonimia riot boiled. H-
The OE m i v m.
nea: ftringentes, decuflatim all dcfenfionc genuine fefe cutting-ing, that form a network of understanding of the lub-catapults Rcjiciendu <; verb is a nefarious art abuf with fubditoruminnocen outlook at liberty, crafts cruelty bleeding cast irons. Intra-cation quxftio is a matter of common-ment. Nonubivis world faxa reperiuntur, as on the fillet Melite New City, from Speclino defcripta con-ftrudta nature of these stones, that is, utglobos tormentoruminnoxic swallow. Nor is that finding that, quii, were about the city, to the number of poles in the distance, the flint-stone exposed the whole line, so that fpem and-cetfuum they have to pay, he ubique the argument, indeed, in the same place Infulxillud peculiarenaturadedit, such as is made by a little bit-run of the feet of the depth, or by digging yet higher, the flint-stone you to reveal, to whom the land of the fupernenaturaimpofuit . Stones, marbles are not alone fiimtus im menrum accumulate, but also Machine-rdare wanted. To deplore the veto, it appears to fpedraculum, they go to cities for-potentcs, folc cast up a bank &: fofsa, abfque towers and fefe the coronation of the ft as efle glo-vary, it is not providences of the whirlwind of war, threatened as it was, it is certain the ten-thousandth the innocent; the outlook at the same, & folc difpergenda built a fire-wet fuarum faftigia. This very, feepe damage provoked by the long-Dion former roleratas forget-me, too, mistaking; fecuro meanwhile, quodabhe-heroic ancestors neglect, cruelty should be exiled, adcoque end-sup exceeded obfefla penalty will not, however severe winged vidoriam porcarent, military and boundary inadvertently, oliin ftrepitu diflultantium deserved to win in learning; except where the horror-obfefla incutcrent, to apply force pr?dentia nefeiverunt. But adeem must, formamoperum fufius explained. If you have any questions about procminentia fltus Munimentorum Inc, and play the best we riflimumfitum-eflcjudico, flat surface where inflar promontories on vaft
mare.um fulminantibus are cast off by force, defenforibus fua the damaging hail,
P R O ob 1000 1 5 IT.
sea, like Fliflinga Zelandix dislodged ?voc?rit; neighbor, which is by the river with a wide & deep, from the duobuslateribus, autab one part, and sanction.
But an order of such a fervabo; Geo-mctricummodum five Arithmeticuni diceremalis it (the object) prxponam, such as higher fundamental mental impofitum; proceflumfub end of this mechanical fubjungam.Geo-metrics, however, limit the quantity diverfitate commenfurationum-fiderat. The first consideration is linear, which is described in the first book abfoluitur, Secundd fcquitur pianos give the same
| K longitudinefcalamconftruere. 5
1. | Theorem. ScopeacciditutDefen-
SL-u * ^ 3 ft0 of ttna pet it a straight line, the other barely there. 4
5. Theorem. Defenjio demonstrated the best all-Jlratur. Ibid.
Of Works smaller. First of Redu & Affairs.
4. Re due his delineate. y
5. Reduftum [upputare. 6
6. Reduftumextabulavelfiipptitationedelineate. 8
7. Reduftum field delineate. Ibid.
Secundb Star.
8. Stella delineate. 10
9. Stellamfupputare. Ibid.
10. Stellan on board velfupputatlone delineate. 14
11. incampo star delineate. Ibid.
** z Ter
Index
Tertib, DeJineationes Caftellae half was flat.
II. CafeUorum cum'Dimidiatis protection in-
vent ™. 15
i j. Castelli half turret cinlla, fuppu-
settlement. 16
14. Caslellacum half a turret on board
la or fupputatione, delineate. 19
15. Castelli, with half the field of defense
delineate. 10
DcopcribusMajoribus. First of rcgulari.
16. Tigliras ACUTANGULA protection cinilas de-
lineate. 16
17. The turret of the rectangular huts Sylvia, deli-
neate. 30
18. Religious Supputatio Delineationiim figtirarum
Hum. 3 5
19. Pigtitam regular boards or fupputatione
delinearc. 45
yo. The tabulisdimidium or completely velduodi-Midi turret delineate. 4 4
21. Castelli to regulate the field M.unimentum
delineate. 4 ~~} viartim.Horizontali & cocperta.
• magiiiis again and fojfa association. 84
The ichnographia.
8. The method fupputandi Ichnographiam reduce us 90
9. Brazil Ichnographia Re ductus .ex board; on paper and on the field.
10. Supputatio Ichnographia Steur. 94
11. Stell vrum Ichnographiam from the board, the chart #
And in the field to complete. 9 8
goes. When a mixed mode fupputandi Ichnographiam Cajlellorum propttgnaculis. ibid.
13. Ichnographia Cajlellorum proceed with the halved
battlements, confeftio. 106
14. Supputatio Ichnographia Cafiellorum quadran-
such dimidiate. 108
15. Ichnographiam quadrantals or dimidiato-
Rum Cafiellorum boards complete. 1 2 1
16. Ichnographiam ¾ of a government fup-
disadvantage. 115
17. Ichnograph'eam Newcastle Dodranfalis or allegiance,
Or protection also Proptignaculi Simply put, the chart or in a field sketch. 13 8
18. A recommendation from Ichnographia figur. irregulariii. 139
19. foffa Reduct whether Orthographie & # Ichnogra-
ph'tca fupptttatio. ibid.
m. RojfaStellarumOrthographica & Ichnographica fupputatio 141.
21. fupputatio the same Cafiellii to halve the tower. 14Z
11. Sup-
Propositionvm.
12. Supputatio fojfe lebnograpbica in cafed Ouadrantaltbus & dimidtatis. 145
z Supputatio lebnograpbica fojfe the Dodrantali-
Reglis the bus and shapes; 14J
24. Device Injlrumentorum quibus ASCENT-tea and the steepness of the field.
BOOK 3.
The Stereometria &: Sketch.
Propofido
1. QR Heorema 1. If the body to coat the wall of d?r?tur, which Ichnographta Parallelogram-mum reference, and makes the plane perpendicular '! the horizontal sides abfcijfum, folidttas comprehensively under plane perpendicular Or-tbograpbia, drfub length Parallelogram-ini.
z. Theorem 2. If we grant the solid body of the ramparts, and the planes of the, adHorizontemperpendicu'aribus, utrin-which abfcijfuin, of which the Bafia The triangle is fuerit-, it may be a solid-cularibus' Illud planes perpendicular to the Horizon, in the various bodies, of which the foliditas from the multiplication of the height of a BAFTA in the same bodies, or a part of the height of, or at the parts, producipoteft, fecaripoterit. 157
5. The solidity of the body wall, the solid triangular track down. 161
4. Theorem 5. SolidaTriangularia external, son Ortbograpbiam retaining the same, are among the
** 4 feut
Index
Safes may be that the remaining kbnograpbia fab-tend. I71
5. Theorems 4. Solid triangles is internal;
Ortbograpbiam retaining the same, equal to each Bafes so that the remaining sub-khnographia stretches. 174
6. StereomctriamRedutttiitmfupputare. 178
7. Stereometrica fupputatio stars. 179
8. Castello as a bulwark Dimtdiatis
Stereometrica fupputatio. 181
9. The method stereometriæ Caftellae quadran-
of such things, or of the half, abfolvendi. 18 6
10. Stereometrica fupputatio Castelli ¾;
etiatn Caftellae productive than the king, and Mu-nimentum defenses and flat-fupputan appropriately. 194
11. Theorems j. If SoUdumquadrangulare, which
altitudiniaqualts equal length, made-to Hortzontimclina plane dimtdium right angle, difttefcetur into two parts fourth slits SOHD superior, inferior Solid below d?citur, fupputatio verb cujufque body crossed-pofittone third bujus almost completed. 21 o
1 z. 6. Soltda fttperiora theorems of the same Or-tbograpbia, in which the proportion accliuitatis ESL, funtinter feut Bafesftveltnea which solid on a Horizon finishes. • $ 21
15. 7. Theorems solidarity of the same or a lower-thograpbia, Dr in qu'tbtu eademproportioac-clivitatiseft, are among the feat Safes, five straight line, ending
Propositionvm.
Parallogranima ending the bodies of a severe-nzonteftiperponuntur. 218
14. Concrete fuperiora of the same theorem 8. Or
thographic, cqtialem line for Bafihabentia, feddtverfam breadth of ascent, there are between [cut Those latitudinesacclivitatum. 210
iv. The theorem 9. Concrete lower levels of the same Or
thographic, in which equates llnec Baft sub-nets, but the width acclivitatum diverse than, equal to each other, as well as the broad-declivitas. 211
16. Portarumprooperibus little discovery. 217
17. The gates of Castello Quadrantahbus & Dimidia-
tisinventio. 228
15. The gates of Castello ¾ of King & In-
"Ventio. 229
19. Porta for Munimentisexemplum. 230
20. The method of inventing Sohditatem, quepropterpor-
and from [i bliditategeonietricd eflauferenda.i Example 22 Pontispenflis. 244
22. Conftruflionesaliaadporta-spertinentes. 24;
23. Example Downsexcubiarum, which generally va
.item can Corps de Garde-quarters Stationuni. 247
24. The method of solidity comniimem information, or
requifite ground. 249
25. The solidity of the two men thief pm, fecund
How folvitur back. 250
26. The first ufus stereometriæ, fupputationis, fump-
Tttt mdicatio. 251
** 5 2 ?. DittoIndex
27. Data FJumero operariorutn, fumma days;
what to do any work performed pofat, indicate- second U / stereometricorum us. 2F2
28. If the time is given, the opusnecejje ejladfinemper-
led indicate how many workers requirantur-, three-tiiis ufus stereometricorum. 25 3
29. The method foflam so difponendi tit country where EXT-insomnia adconflruclionetn fufficerepofiit, and fupputationeStereometricapoftbabita. 274
30. Stereometrica fupputatio foflc Reducluum. Hi.
31. Stereometrica fupputatiofojfainStellis. 255
3 2. Stereometrica fupputatio foflc in Cajlellis to halve the tower. ibid.
33. Stereometrica fupputatio Fofla the Caflellis Qua-
drantalibus and the halved. 25 6
34. Do the village Stereometrica fupputatio fojfe
drantahbus, Regia and safeguards. 162.
The foundation outline a common reduce us demonftrantur. 268
3 &textus>numerorumadminiculo attentd adhibito conjungi. Tyroni auteni autorfuin uc omnes liguras, qux hie cxigua magnitudinc dclineantur, in majorenx forma m trans (era t: qui verd frudlum (olid uni pcrcipe-re cogitant, illi fupputationes etiamimkabuotur, & exempli cum tabulis confcrcnr.
16. Ortbographia. 297
Article 17 ichnographia. 298
The work exrcrioribus.
18. ParmulafiveTriang.Celerrimaconfiruttio. Hi.
19. lune Fort acutangulo praflrue-
things. x <) <)
20. Opera Cornuticonflruttio. ibid.
21. Operiscoronaticonftruttio. 300
22. work
PropositionVm index. " ix. Work heart nut nm, and op ere behind coronal
niunire. 301
Some OfFenfiva.
23. Obfidionumgeneralifiima dijfofitio. 301
24. Caflrorum muniendortimgeneralifiinia. 304
25. Caflranietationiipedeflris foundation. 305
26. Caftrametationis equejlrufundamenta. 307
27. General Caftrametationis example. 308
With 28 feet to the lines circumvallations. 310
29. Works inlineis intermifcendorum confectio.il).
30. Qaomodo Obfidionis from field to form alicujuf
Cbarta business. 515
31. Example Suggejhu gun. ibid.
22 Acceffere dufluo. 517
33. The vineyard leviteradumbrata- form and re-mines
quifita. 520
34. Obfejforum refuge. ibid.
To LE CT, MASS.
"T \ Ivis Tin is opufculum into three voluminaj Before ? ^ - ^ text Five prob" ecepta compledirur the one-ta stories, tertiumfigaras: When cnimmoleftum happens, figures and tabulasatcxtuiejungi, can this rationetabula -> text> numerorumadminiculo attentd applying affiliated. Tyroni fictions all liguras autorfuin UC, which exigua magnitudinc dclineantur here in the form of majorenx m across (T era, who counts the fruit (olidis one pcrcipe re-think, they fupputationes etiamimkabuotur, and for example with the tablets confcrcnr.
ar
MILITARY
Children.
The Delineationibw.
1 t i n e f 1 1 Brazil, to the H-1 / nearure from the outer wall,
starts, defcriptio.
z. Reduiftus is needed reinuSjCujus Brazil Quadrature reprxfentat.
3. Defenfio is an difpofitio lines in the figures and that latcra aflalientium to iftum patefcant.
4. A simple, indeed, which is granted by the side of the thing is done; ge minatavero, qtueab Each.
5. The star map which is less need for tax-ftellx report.
Square turret ftintquarformam trapezium hold.
7. Caftellae halves of the towers, and there are smaller works, which are protected by such a bus for protection.
St. defend themselves are intact, which is four
A line
? • Book 2
delineantur lines, and the shape and angle of vcllinea rcdla adhere thereto; poftcriora ^ ula flat, however, are said to be on the battlements.
9. Caftcllum cfWpus less force than UC copiofa refiftere poflit host, such as font, which is not yet king on CEOE, & royal quadrats, and the pentagon, may also DimidiaSexangula end of the court.
10. Regis Caftellae font, in which Defenfio iftum Tclopeti terminated. Dodrantaliacum Defenfio ties fourths longicudinis Royal penetration. Defenfio halved since the half-longicudo Royal dcfenfioniseft.Quadran are such that: a quarter of defenfionis prxdiftse ship. Rcliqua Castelli called the intermediate poflunt.
11. A fort is figuramunita, quaefor-ened fuaexercicui-fated numerofi rest ftcre poflum.
12. munitions ACUTANGULA call, which has an angle-bent turret acutumj area of ??UC & sequences figurx, so-cangulum of the last Acurangulorum Munimenrorum cenfebitur.
ii. Rcclangula Munimenradici poflunt, which is a corner turret Rcdtum UTA passenger Duodecangulo reliquaefigurse.
14. Figure Rcgularis than that: & A: quilatera & A is? Quiangula, the cot turret exact number of angles and all PropugnaculaSi-thousand and an equal. figure
A P S 5 1 1000? $
5. Figureirregulares Ordinary own wells, and is made of two figures is a rule laid-buscompofitio-the paternal hearth; circiilis to the oblong shape of the AUC and the Fort regnlari piano, as in Figure-s (ecundum & tertiimodi.
X6. Figureirregulares inordinary funtjn the bus compofitio is made of many more than two-forms who have to defend themselves.
PROPOSITION I.
T> AT & ^ one line of the same length with dintfcalam * / lrucre.
F 1 G v r No. 1;
Cit given length liney AB feptuaginra '-'duorumpedum, the line is long, 100 500 and dividaturin aliquotpartes, hocmodo. First-fumatur a pair of little power and de Cic-line naturfuper veifiis 500; Ten-capianirlongitu such a party together, and sometimes they put unto the 100, this line has already fupcr 100 500 numcrentur parts of many foot rot eftlongi-Tudor B uthic72, Quy produce EF fupcr this EF conftruatur triangle / polygon-run EGF, have also a length and abfeindatureadem diftantia G & G through punfto H1 straight draw and a lingulisli-nexC 500 pundtis linear lines vcrlusG, such as a line of hi leadeth suited erirque KL is the length of the ladder datx AB & a thriving.
A Book 2 Eadem4
For the same reason, line A B is given feptingentorum the operation of the twenty-fi is inftituenda of the feet, the feet of fignificabunt unless beyond a belief at that time in the smaller particles of ten lines k, majoresvero a hundred feet of the reprsfentabunt. It should be noted that the role au-tem lines 400 is always greater than 50 K lines are required.
Near the mouth of IT IO 2.
Theorem. Sape is asking of hardly one in a line of the next, it happened that there should be, on the one Defenfio.
F 1 5 G L A N 2.
TN Figuraapparet, quodDefenfioapparen - * - terpetatur from the Pundle A, and A inferiptum aliquapars lines to which it is, seems to be to defend the line 400; ft width of lories perdition is to defignetur I forbid you, be applied in line with the Defenfores for an interior, it becomes evident that the total Defenfio lines 100 500 and from a line B, B ', B, B', q.e. off.
PROPOSITION 3.
Theorem. Defenfio best of all demonfratur.
F R A N G 1 "3.
The figure shows how the Tennessee line FE-ten defend the seat, thus drawing HI defenditura defenforibus fignato A; A line G, a defi-n-foribusCfignatis is protected; LineaFGade-fenlb-
from
A 5 1 1000 P St. 5
fcnforibus Bcuftoditur; I say this defenfio-end optimamefle, judiciopetitoexlinea ON when enimhoftibusibt acccdentibus harder and to a greater extent than other relifis poffit (ie comparison of clove-like and, diveriorum, bearing) aflerendum best efle defenfio-nem.q. e. off.
The operibwminoribus. First of Redutdibus.
TTl Redudhis defenfione jufta deftituun-Atur, and therefore kept the charge of the contrary, are said to be, than to run the risk of. A square! are aclatus have aquadraginta o £ to the one hundred twenty feet. In these two should not be Delmeatio-ing cubes shape and length.
PROPOSITION 4.
Release the sketch.
Fig v r from No. 4.
? Clguraquadrata possible, and latus48pedum x ICAL confeda.ex the same defumo 48 feet, the length of that fumolineam AB or from a command over this Geometriacqua-square conftruo: critque project from perfect. • •
A? F R / O-
6 Book
PROPOSITION V.
Reduttum fappHtarcs.
Figure NQ V.
T TIC names Pundornm, lines, or * ^ individuals are pnenofcenda. A point is a long-center. B, 100, 500, R U zip funrpunda Fig. From 100 to the beam. B 100 sideways. B E diagonal. BA 100 the center. BCE figure.
There are regular. i. The center prodir di vifionc whole number, five360graduum by four. For when you were a figure is made of the squares, in which the neccllario the four sides are of equal worth, crime fubtcnfae BC and CE is to ED, and DB are not equal, they will have, however, fubtenfae acquales, on the same circle, too, azquales of the arc, and therefore the arc BC will be Quarrer a part of the circle, of the Arch of the BC, it is being measured the corner of the BAC> therefore, even in a part of the angle BAC is composed of four Redis eric Quarrer, and therefore alighted on.
Grad. Circuli.90 BAG Angul.Ccnt. Legs.
Figure 2. The angle of the center fubtradione is produced from two litters of five angles of 180 degrees. At every corner of the triangle of three two equivalent return, then ablaro believe BAC refide two ABC & B, 100 A .: I believe are the equivalent of one triangle BAC and CAD requalia through trialarera xqua-
lia;
A 5 1 1000 P St. 7
liajadeoque Angola From 400 squall's angle, and two BCA ACD equal two ABC, BC A quiduouni rctto sequalis funr, the BCA DCH together, five-bed CE uniredto equal to the brief, when the shape of-squares fit, nccefiarib corner figure the definition quadracus, Rédl be.
180, two right angles.
90 the center of the lower part.
90 angle :.
j. The premiflis fcquitur Triangle B AC efie redtangulum, but for a, 100 by the beams are of the same circuit Eric triangle Ifofce-les angles B 100, B 100 From equal, and that one redtis equivalent femireCti, or 45 inveniecur icaque AB and AC, Linus.
He who mul.tiplicanis by the sine of the angle ABC, longicudinem AB 48000 70711. ^ 4f Graduum3eft.
Prod & gives um 3394118000.
Quod divifum per finum to turn 100000.
Dacprodu&um, lineam AC 35941© Ac.
4. Diagonals nihil aliud eft, quam Radius duplicacus , igitur duplicanda eft in n-ta AC,prodibic BE. 35941 ®
Duplum 67881® B E be. In tabula Operum minorum qua: parte 1 fe-queturlarerafumpta func 48,71,96, & 110 pedum,in Rcdudibus.-quiquacuor Reduflzus in mode Geometricofufticienc.
A 4 PRO-
8 Liber
PROPOSITIO VI.
Reduction ex fupputatione wet tabula, delineate.
FlGVRA N’ VI.
T? X fcala fumatur longitude Radii redudus;
fiatque hoc intervallo circulus, latere vero ex fcala defumpto fecctur circulus in quatuor partes, pundtaque lineis conjungantur, habe-bitur quxfitum.
Tabula cujus in hac propofitione mentio fit, reperiturparte fecunda folio i.
PROPOSITIO VII.
Reduction in campo delineate.
Figvrte amb^ N° VII.
D51 ici via hoc fieri poterit, velex centro -‘-"'vol finecentro.
Si ex Centro, collocetur Inftrumentum in pun&o pro centro eledto A; fiantque anguli refti B AC, C AD,E A D & E AB: Radii vero E A, B A, C A, D A,ex tabula commen-furenrur; pun£taB,C,D , E , palisfignatalineis conneftantur, ac line# effodiantur.
Ablque Centrouno latere defcripto pro longitudine data, ut AB,ad angulos reflos linex A C,B D gqualesfiant ipfi A B: & CD conneftatur.
Secundo
P R I M V S.
9
Secundo de fie His.
t 7/E confcederatis Belgis rariores fere ex-•*- -^truuntur quam Hifpanis ; area interior artftior eft, & ampins circuitus: longe tamen meliores funt Redudibus, quod defenfronem habeant.
De Defenfio ne [tint Axiomata. gener^lin.
i. Eminata defenfio fimplici praefertur.'
z. Quo brevior defenfio co certior.
5, where the slanting defenfio sharper.
4. Where diredior veroeoiatior.
5. Defenfio idumlclopeti neexuperec.
Pofulatum.
Tennessee defenfioneconcedendum eftexperientia - * - fuffragante, idlum fclopeti and the reality tends to six hundred feet higher, to prevent the ball-valloemenfopaulatim weakened descended; provided however that the so-fifty of the feet so that feptingentorum diftantia, still a force against another: Are defenfio longiflimis ufc¿; and fifty feet to the feptingentos is concclfa.
Data in their orbits require three: The first figure or square, or pentagonal or hexagonal shape; Secondly side, which among other ends of the side-redmftuum ??heels sucked, ame turns of the thicker book
tion the corner of the Defenfionem the least of them, quem hie fumfi of fifteen degrees.
PROPOSITION 8.
Of linear stars
F 1 g v r No. 8.
/ ^ ^ Rfiar Eometrice autraechaoice regular shape, uthicquadf3tuni H ie A. cujuslate-Ra (ecundumlongitudincm despite late exfcala defumantur, uthic 100 feet from pundo From the figure at some distance (less than or equal to half a ramen side) inside the arch defignettir B. and radius AC, from the center 100, abfeindatur CB rainbow fextapars circuit ideoquefexaginta degrees here arch is divided into four parts, one of which fifteen degrees er it, 400; du © 5597 -
the
A 5 1 1000 P St. J
The FC inveniendajln same triangle of becoming cans corner F-100 G ijgrad.eft 10352.8. What multiplicataper CG is half of the latusfigure 50000®
He gives Produdhim y 176400000.
That divided by the radius of five and no end to-100,000.
F produces 100 51764 © • CF *
3. The triangle AG 100 CG ray AG tangent, Secanseft A 100, half the figure, a 100 G whole angle above the figure is found, then half hidden. From G to find. Tangent of the half angle figure, here 45graduum, is 100,000.
What is multiplied by G. 50000 100 ®.
Datproduflum 5000000000.
Quoddivifumper beam 100000. gives AG 50000®.
From 100 to find. ACG cut the corner, here it is 45 degrees 141411.
Quaemultiplicataper G 50000 ®. He gives produdtum 7071050000.
That divided by the radius of 100,000.
He gives the length AC quaefitam 70710®. and,
4. A smaller radius R, G fubtradione invents, was found by a G, is left.
A G is found 50000®.
SubtrahendaeftFG _ 15397®-
ReftatAF
In the same way rcliquit ftellx fuppurantur, in a way
14 50 1 8 1 R.
however, the numbers duly fubftituanttir.- board Delineationis Stcllarum the second FC-forever it.
PROPOSITION X.
A star fall from the tabula-, velfupputationet dclinearc_y.
F R A N G X.
EXfcala the beams of their defumta, let this be done by another-in the circle is, moreover on the Periphery of the side of the cirumponatur as often as neceffitas of which requires, moreover on the periphery of the inven-cxpundishoc tis way, the length of the OF THE FACE, the bows of decuflatim they are done, and the mis-Peripherie pundtis punftum connedtantur found in this manner with his neighbor secretly. The table has, the part of the fertile, and they Folio t.
PROPOSITION 11.
Field star deltncarf ^>.
Ft G L A N 11.
TJRimolinea defcribatur, better qualongi x-rays of the larger size is assumed here inftrumento over half the angle of the center-number fields, and in the corner near the center defignen-tur Linearveroalrernatim be equals, the Rays nempemajores and rays lincis Conner & minores.Extreixia rays will be disclosed.
tcrtio;
A 5 1 P 1000's, ts
T'ert 'TO'I Delinedtiones Caflellorumcum half was flat.
ThatTroy fated frequcns ufus is called the 1 -1 Redu and fight us with half-soled; habentquc defenfionem dimidiamfivc simple and better than ftcllae.
Side of the size of the one hundred and twenty, until the feet should be given to a hundred and odtoginta can serve. Now that the four-neceflaria are given here. First shape than a square rather than another / Secondly, the side ends pr & fcripta. Defenfionis third angle is smaller, thirty degrees. In the fourth proportio line: It was situate it on the side, namely, that it takes place on the third part of the latus.
PROPOSITION 12.
Castelli half Proppugnacu invent yo-Us.
FIGVR from No. 12. •
100 500 100 Vpcr its given latus, f on this point of the feet) by which the square of it done, of which, by means of the side AB in the three parts of the xquaJes fecetur * E and F, E O be a certain amount of Eintervallo defcribanir; exhocarcu, eodemintervallo E o, abfeindatur G O, check of the bow 60 degrees, GO, hiedividendus is in the duaspartes xquales in H, and Eric one of the H O, 30 degrees; E through H & Dudley lined with IEB angle of 30 degrees; jämför B proIon-
g Liber-
Longeus, abfcindetur through lineammododu- £ well in 1: equilateral triangle on a Bi-run conftruatur K1B; duda K F Eric F Kib dimidiurn fortification. 100 500 prolonge-namely, that becomes an equal 1B 550, 500 and 50 of the interval-lo 500 Larco, a ducftis 1000 N & N 50, According to the Fort Eric conftrudum; to whom be left for: qualiafiant. |
PROPOSITION 13.
CufielU dimidiate Propugnaxulis cinch fupputarc.
Figure No. XIII? VrOminaPunftorum angles and lines rumpraenofcenda. A pundum to the center. B, 100, 500, R punfto figure. F crimes nozzle. G pundhim Defenfionem. A Pundle AU. 1 Pundle tower. H F Ala. A beam is 100. The side B 100; which third parties BG GF and FC Neck line. 1 100 prolongation of the side. Ill make. KG is part of Defcndens. A lineaftrin-G race. G. defcndens line. BAG angle. Center. CE angle. IGC angle Defenfionem. Here the angle Propugnacu li. FH angle made 6c AU. For the excmpl deturquadrangulum, of which no side of the feet, the angle of Defenfionem 30 of the Steps, and the line of the neck on the third part of the latus.
P R 1 5 1000 S. J7
Kings fupputatlonit.
T \ angle E i. ? ^ qtiatuor produced by the steps divifis Cencri an angle B from C.
BAC.
44 J
2. This fubtrado figure out the angle of 180 degrees is produced.
180
90 BA 100 fubtf.
The angle of figure 90 BC.
5. The angle of Defenfionem 1 100 are given two 30-gram, hocfubtradoex9O Degrees (umma that the two acute angles G1 and G 100 100> 100 G Triangle redangulus 1, remanetangulus propugriaculi A 1C, which xquatur GHF of parallel h f, 1 C.
G & G Total 90 100 1 100
Jo IGC lower part.
Aug. 60. PropugnaculiHIC, GHF '
Auferacur F G H 4 out of 180 (umma two angles G H F & F H 1, re-mandje angle made F & ALS HI
180 Total GH.HF and FHI,
. 60 GH.HF fubC.
FHI angle made and no alarm.
Regular Lines. 1. Side B is 100 to 110 feet here with side divided by three erit- 100 H- F ^ uColli, to BC and GF-Fane atquales
? ill b
AB.
PR.
GH
HI IC. KB.
18 On
** $ 40 {F 100 line Neck, Item BG and GF. 37
2. In the Triangle RC & angle B to C, the remaining angle equal to half the Figurx: igiturper SinusinveniaturBAvel AC or BC Latusenim is given.
He who multiplicatusper side BC of the sines of the angles BCA 45Graduumeft 707m, the same is 120000 © Dar produdtum 8485520000.
That the whole of the Gulf of divif 100000. carry her through the lines AB, to which for the sake of the angles ABC, B, 100 A, has equal, arquatur also A 100, and the other. 84855 © radius.
3. The triangle of GFH, pofito Radio G F, and H is the tangent GH fecansanguli HGC Dcfenfionis; and £ 01050 °.
The H invenienda.Tangensanguli HGF50.
57735. Multiplic. By GF above the inventum © 40000. Prod & gives um
This divided by the radius
It produces H Alam
The GHinvenienda. HGC and the angle 50 °.
© 40000 115470. multiplied by the GF.
He gives Produtftum 4618800000;
llludque divifumperRadium 100000. give GH are Stringentcm © 46188.
Mister G is equal to the conftru & ionepne-retired, he ic also shewbread A 1 K B.
4. somewhat G
23O94OOOOO.
IOOOOO.
© 25094. O
A 5 1 1000 P St.
4. G duplicatalineam
• T * wife
if)
G lieft 4618 (3). Or
Def. G. dabit.nempe n. 4
GH Htfowl F] DuplumSxJ7S®.
f. K B & G addict give defended ,. RG.
MB fup.arqu.HG 46188 (3).
BC tert.parsLat. 40000 (3).
RG ~ 8Tx18 '© .kc'
PROPOSITION 14.
Castelli was halved Propugnacttlis the Table welfupputatione, are out of line.
F1 G L A N X111.
TNtervallo rays from 100 of the fcale defumta round-xculus defcribatur, Deindc side BC fupec circumferenria quarter basket and draw B 100, 100 W, 500 W and 500 B; on the one side at the distance F 100> is obtained from any pundo figure, abfeindatur moreover on the two sides do by a continuous line of the Neck; FH is perpendicular to the length of the hinder part of the pundtis of the Neck ,. After prolonged length of 1 100 ten- side-Ganda than once, and HI ducenda.atque fic in the rest of defense, until the entire project is perfc & A. The board is part i. T leaf.
B I pro-
PROPOSITION XV; .
Cafiella with the halved tropugnaculis field delineare_j.
Figure No. 14.
Of the center is to be elected, the result being that here, according to A lines AC longicudine The rays of the defignetur, dcinde angle of Cencri Bacco inftrumento woven together-be maintained that, and again, the radius AB, is equal to the prior of AC, and the angle of the center of EAB, and the fie forward. • out-cremicates of the Rays, connedlantur with a line, uThi BC> EB, DE 600; abfeindantur fupcr these lines, the lines in the Neck, FB, GC, and, DH and EI, Now, from the punctum F, G, H, and 1, perpendicular to the erigan-tur the length of it, Ate, quxfiniuntur at O, P, and Q "* R, TandemInters a debtor to the length of the pro-longanda are Lines finientibusin IV, 50, 1000 N; effodiendos be linexKG GP PL, H, Q, MQ, 1001 RI, NR, and N> fo> OK and habebiturquxfitum.
N o t A.
Tantadiligentiaquidem indigerenr smaller bag is not much here to dissociate fed through utgradatim Caftclla & mu-nimentum easier to attain Methodus in front-fpicio easier requirerc videbatiyr. But because such activities are incerdum fubied building efle, wee action is undertaken funr times fuppurando confer-y but then the board lequens adhi-
can be used. Queries know their works and for a long time-turner of the duration of deftinatione conficitintur, I would rather fupputatione or by the documents rather than those which mode a Mechanic, On the not so often the same thing is a faultless-cauda is made, this one once I warn you, modern geometry-a price ufui efleinillis, which is almoft anerniratis deftinatione conficitintur, a Mechanic, however, sometimes, for celcritatera utifuadeo.
Map-Huepertinet delineation of my goods. 2. part of a leaf 1.
The O perib vs. maioribvs.
First of Regularilom. ? plgurae with its preferred hang-x anteecdentibus are described, both in size and form, which flanks figure defenfionege-contaminated screening.
The axioms of strength and cost have to be considered here.
1. A NgulusProptignaculi becomes even smaller (e ^ ? xaginta levels no greater than Nona-
About forty degrees.
And fifty-five hundred men of leptin is made any more, not even the feet of the 2. Longiffiroa defenfio.
F1 g v r No. 10 V.
The names of the corners ^ punclor
And the line.
50 is a punctum center. 2. K, O, item 1 B 3 func
2.1 BOOK
pund'aGgur # font. 5. H-point font S & P also give better protected. 4. A and B # $ pundta Neck. 100 and 500 pundta Ake. 6. rattles Defenfio-nisF & E. 7. Spread your wings stops G & Q
8. Panda Pcrpendicularmm IM & N.Anguh font. 1. HLP & KLO the center, going HLS & KLL, angle Figur # 1KO SC
5 H P.j. The corner turret RHC. 4. An "angle defenfionis smaller, CFA DE.EB that the bus quae * G FL 100 and QP, P. 5. angle made & # Al, HCA, APP 6. The angle of Chief Colli, HKA, PO B. 7. Al corner #
6 ftringentis ac F, B, E 500, in which quae HCG and PDQ.
# Appellanrur line. 1 radio within 50 K, Lo. 2. LarusKOvelKI. 5, line Neck AK BO. 4-A1sAC.BD. 5. make RH, H. & P. 6. The outer radius of 50 A, LP. 7. The Capitals KH, the OP wing Chord # 8, B, E, A.
9. Front, H, G, PQ. 10. Outside H P. 11, Part Chord # AF and B E. 12, lines ftrin-gensCF, 500 E. 15. D. 14. Q & # GC extension of Al Ala Prolongata AG, B * Q. 15. During pendiculaiis 50 M. 16. The exterior of the house's interior perpendicular-DR. 17. Dcfenfio- fhingens H F, PE. I & Defcnfio couftaus HB
Note. # Poffont liter converted to B or BA, and the same line are specified.
A 5 1 1000 P St.
Requifite. Figures on the situation.
i. Ala strings belong to the greatest extent possible is done can serve z. Neck broad line of fur.
3. Defenfio ftringens the shorter the better.
4. Ala, are longer than shorter duration, but Ala string of Alasne-corrupted files.
General Proporiionnm.
Eneral call things by almost all 'ard-approbanrur figs. Wherein J & obftrmxcrunr like laws, are included ver.b-falequentibus rules.
1. make in a regular, never less than half the string is not greater than the wheel event. Yet it is not entirely defpicitur a minor irregularities.
2. Halah, the fourth part of the face is made to be less, or greater than half the fi ve fcmifle ejufdem.
3. Linrea Neck efle must be no smaller than • Ala.
Specialin.
CPecialia to what cujufvis artificispro-teriously equal; most of these vary in a remarkable degree, the ability of mul-tistantum that exercised-the lust of ruin: so that the number of the heads of so many modimuniendi fint. When I bid us Analyfis.propofita does not take place, that is, the part of the .DAT, which of the five quibufvis B 4
24 "Book
given, with appropriate Delineationem fuppu-tat, but adGeometrasrcjiciacur, follicitusfui eliminate as far as my ability, a thin-spun style, suffered, the best way I would have chosen, eumquelolum, not-giedlis others, tradere, Erin is, however, such a
i. You shall also make a part of to its strings belong to dimidiafumacur, so that the propoitio The vibrating string is: to the face of a fit du-pla. The reason cited by this ratio, the sodden things being equal, Ala augmented chords, and the fight-hearted enormium evitctur profufio. Also in plerifque figures tub less environment, and with fewer governor of the confequens> rnajus fpatium defcndatur. Therefore, in the figures of the royal, You shall make ducenrorum quadiaginta the Chord, four hundred and qdtoginta of the feet erir.
z. the proportion Als, eftutilla puflit elledimidia the best part of his face, v el-ta any party to tcit or fourth. When she did not om-nes figure, it is conveniently this admitcant, to use such an one for-greflionc Arithmetic *: * as the square figure of Elam shall give from the fourth part of the face; Qiiangulxextertia-being. Hine ICMP-bliss accredit to the foot, ten, until it is half-part of which takes place in the Nonangulo OF THE FACE, Als, and so in the face of all the fequentis fubdupla is propoitio, fubduplaproportio OF THE FACE adchi-it-same time by the dam; Confequens Chordxad and through face-to-face and reach out to the ratio of the logarithms continuous clef meliorcm to find pofle trust. Eric wing of the royal figures.
A P J 1000 S. 5
In the square, the Sixty feet.
In the pentagon, Odtoginta toes.
The hexagon, ninety feet.
The Seprangulo hundred feet.
The Odlangulo Hundred and Mercury toes. lnNonangulo and lequeqfibus hundred ginc force-wide.
For this reason, Ala strings is made, and the anger and the first main requifite Sa-bills. Line Neck (quoderat fecundumre-quifitum a hundred feet deeper. Defenfio ftringens fterrio) never to five feet afeendir. * Hint, however, were given to war to be from the walls of the wings, prioiibusfiguris dan can not do, unless beyond ineparabih deteniionis the damage, by which the Ala accrefcir by our feet, for the ten, and thirty-six are more than that of a quadrangle, the feet are perishing, in the going to be carried out of Halah, strings belong to; & Defenfio ftringens quadraginra pedeslongius rejected, so as to firmly conclude wings longer than in the prior-bus oculisquidem caressed shapes, Fiona is a defense-proilus coirumpere, utter T m-th manifeftum erir. As may be seen on this account, rc fchema the slits ^ the number of tcit, quodcla-more dear, the gods (5tameafirmabit. It is thickest at proportioncm is concerned, of those, some not-ceflitate of Mathematics of the fupputationejecun-as long as a given figure by it, come forth; one is appointed by, at pleasure, the smoke of the potefl, whom I have chosen, the corner of the PRO * pugnaculij in which, until to the Duodecangulum,
B 5 are inducing
h # c the proportion of Fervat, that the Angle of a palace of the shape of the angle of fifteen degrees of femillem: excels; An-and terrible, and should have no end to mediation by the mediation of that which is in the shape of provenic :, On an addition to it, if the Steps: In a matter-liquor fequentibuf: The corner of a palace of Rcdtuseft, adeoquenon fupputatur, fed by the disgraced; Ninety degrees. Because of this diverfitarem other shape, with propugnacu lis acutangulis way when redangulus gang-morrow.
PROPOSITION 16.
Figaros ACUTANGULA Prof'ugnoctdis and contains some of the linearly.
Figure 16 N9.
F & N fequentes this propofitions • * que given five (unt • things differently from others to smoke, anger, however, that one of the five were given nullumab dcpendcat, necalrericon-crarietur. I will here. i. Formatting. i.Faciem.
Chords. 4. Alam. 5. Proportion of the corner tower. Another example ferviat Quin-quangulum Regium5cujusdaca above the fuerunc propofita; has been rich in the norm of Figure unto the Duodecangulum is a combination of this, the wrath of the that there is no other, is made in the conftruitionc Ala alone than in a difference of 5, which is as great as you please, in which the force of the shape of prxfcripta is so great, in the first 'k', 'c', however,
Ml.
however, this fcale is selected, or to draw from the line # Cognitx defumuntur to inRegiis' figure shortly before he gives where: (ecabitur line EA at O ??distance from O AG, abfeindatur KO KO bifecetur arc at 50, and then the whole 60 degrees to 30 degrees dimidiusveroL Oh J Bow LO is again bifecctur in 1000, it will be OK 15 degrees Finally arc MO bifecetur in N will be NO 7 degrees and a half. Then arch Nike, which metiturangulum figurxbife-ceturinH, eritOHarcus half the figure-rsbifecandusin 1 to 1H fur quarter of arch angle. 5umatur dividers distance Ni, which includes a quarter of the corner arch Figurx and excelled 7graduscum di Midi,
inidio> and for this we intcrcapedinc / from the center of H abfcindantur the bow of PH and HR, and Eric the rainbow, PR k of the two of the four of the angle of figure & they excelled them twice fepr & of half a degree, or what is the same is, femiflis of the bow of the angle of fi gure adjediisquin-, twelve steps, that & is the case, the proportion of the corner, propugnaculi, fiigio led PA and AR will PARangulusPropugnaculi and comprehcndentcs lines, make better protected 6-retreat. Perpundlum inlineam A 10 R perpendicular to it is a question, that is to say S Q, better than that, the length of wing: from the ICAL defumpra, amcindatur RS: I'm The bowstring, and then in the fcale defiimpta, abfeindatur QV; // this line Q has to be made upon the Rechmgulum
• T QJ / t let VX tequalis A Q> 5 abfeindatur wing on a line of T S A priori sharks from 10 to extremirace of Als drawn faces. Over half AX is perpendicular to Zy and from A through H line is drawn abfeindens per-pendicularem through Z, and Z is the center of the figure, since defcriptam circle and Dudley T b, and the S side, so fignetur in the circuit where -tiSs figuraexigit and latcra results. Propugnaculaita made up the rest of the distance from S or T, b, c abfeindatur d, o E and perpendicular. d eg, equates to S R from punfto f, and g, h ranquam centers arch dcfcri d?ser?bantur distance FACE AR du <3 h, f> g hjhabebitur qusfitum.
Lcmwit.
Theme.
Figure No. 17.
101 ^ propugnaculisRedangulis5proponio shape of many of the corners are protected string face comes to the Diagonals gitndinem has a long-square-over hacdefcrip tijproducetur of connexionspundorumAlae, the shape of an equilateral and equal angles, having doubled the number of sides, and which has huit shape inuhita.
When the square is equal to RH HC arqualiaGnr, eritetiam quad.HC twice fumturri equal to the square R H> M 100, together. Is equal to the square of RC line HC is, however, by the penultimate of the first book of Euclid hifce quadratomRC; 100 is equal to the square of H & bisfumto quadraturn diagonal AB, the squares RC AB between feaequalia when it comes Redan-rectangle of 100 ABD will be an equal to 400 A, B, A 100, 400 to each equal; the same to the rest of near-gnaculiseft Demonftratio; is made from the connection of the sides of the shape, which has, therefore, is yEquilatera. But it is Dudley iEquiangula the RW 100 \ ciebus RW TY, also Alis & W and Z Y.Z.ac string.
I say this from the five given in the figure of efle, a strong beak above the propofitus. EU to shape the e duodecangula. The vibrating string is 480 feet. A PI faces 500 or 100 W azqualis half of 1000 and therefore the strings belong to 240 feet. Ata, on the basis of their feet Conftrudtione they are not willing quart® parts of the vibrating string is TivelineaeN PJtaque the lines NO. Redha clinics and protected by an angle-ell, 11 F 500 is equal to that in a semi-fcriptus about it. The rest lightly on the Geo-meter verfatus, lupplebic. For the same reason-liquor lequentes figuraepoft duodecangulum. muniunrut, the first B out of shape due! defumpta takes place. However, the larger figure difticilli-dclineantur me in this way.
Tabel '
PICTURE LATERVM FIGVRA-run Ludolfo regulars from the Ceulen.
Pofito Radio iooooo Partte 1000. vol.
Figure. ! Stress. 1 Figure. Side.
Duodecangulum. Tredccangulum. 517. 478. 64. ^ 3. Novendecangul. Viglncangulum. 31> t $. 3x1.87.
Quatuordecang. Quindecangulu. 44f. 04. 417.82. I was twenty-unang. Vjginti duang. 298. 284. 08. £ 3.
Scdecangulum. Sepcendccangul JPO. 18. 367. Twenty-to- triangle. Twenty quadrangu. 272.33. $ 2 ^ 1.0.
? 1 Ociodecangul. 547. 30.
For example duodecangulum conftruxi. Radio innermost parts of the scale I is a thousand-cited articles. The length of the vibrating string is out of the should immediately is the scale of i: data48o of the feet.
PROPOSITION 18.
Snpputatio 'Delineatiouum shape-rtlm Regularium.
RepetatvrFigvra No. 15.
Prxcedente two propofitions U-X bus that is, five UC shape depicted in gang-Near poffit anrequam fupputccur and the so-lincatio fupputadone immediately conferred with POF-100 fix,
34 work e.r
takes place, at another time Temper I would like to, the delineation and peracta fupputatione denjum point, as it will be shown in the iequenti propofitions.
All operations are given prime * Ten Benda, MA-joribus dancur the five figures, the rest of the Rules reperiuncur the ear ufusRegularum more than four square innotcfcat royalty fuppucabo. Are data-peri propofita fiierunn
i A quadrangular.
i. Faces 240 H C.
3. string 480'0). AB.
4. Ala 60 DC.
j. The proportion corner to corner to defend themselves if no Semiflem figure.
Kings of ^ tngulls.
1 ^ A ^ gu US Centers OFF divifione interior *
* ? Gry five 3do9 circuit through numerumlate-run given figure supported. Ejufque femiflis habcturperMcdiationem.
Grad, Circle Y jzS / 90 Ang.cent. KLO, HLP.
44 \ 4 Semiflis KLM, HI.
2. fubtradione corner angle DELAY center cxScmicitculo five redire two angles. >
I am. Coke. red.ang. 180
A Long. cent fiibt. 90
90 Ang.fig. SHPjIKO.
45 Scm. LKM, lhn.
3. An
A 5 1 1000 P St. J
j. On the corner of the fort were to be changed in various ways; the thicker kinds can serve. In the figures unto the first Vndccangulum found, if Semifli corner figure if steps are added. In the figures from Duodecangulo burning, smoke was known by 90 degrees, iterif in the fort plane.
45 Semiffis corner figure;
15 Gradusaddendi.
60 The corner tower.
30 Semiffis of the same.
4. The corner defenfionis produced smaller sub-tradione protected by the gods of half-Midi corner of the figure.
45 Dimidiusang. figure.
30 halved. Ang. Fubtrah better protected.
Aug. 15 defenfionisminor. CFA, GHC.
5. moddi fiibtracbo finding an angle of 90 degrees, the angle Prodibio AlaeSc ftringentis.
Grad.fumma duor.ang.CFA 90 and Arsenal 15 100 C A lower part.
75 Ang.Alx & ftringentis ac, HCG.
6. This again fubtra & O from the 1S0 degrees, summa five straight two loops; Rcmanebit angle made and Aire.
180 apex of the triangle. HCA and HCG.
7 HCG fubtrah.
105 HCA. Ang. Causes Ah.
7. If .femiffis corner fubtrahatur figure of 180 degrees, reftabit Ang.Capitalis and neck.
100 1 180 Sum
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