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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 54, page id 797435492:0090
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2 B C Y. VII.
ducatur C FI I. ad R S parallela; erir inFExCepta HIL (quod requiri.
EuIK) aequalis ipsi Z. Nam connectatur CC; e huic perpendicu.
laris ducarur C,T; ad C F proinde parallela. Quia jam anc. C, C Y
COR = FSH, liquet rectangula trigona C CT, R P S aNI-
milari. adeoque fore C T. CC:: SR. SF. item (ob limilitudinem
criangulorum C OHI, SF() est CG. VHI :: SF. FC. cricigi-
TuF ex aquo CT. OH:: SR. FC. (hoc est):: FC. T. verum
eAt CT. FG:: CH. FHI:: HG HL. permutandoque CT. 11C
:: F C. HIL. Quare FC, Z:: F C. HL. liquet igitur HL ipsi Z
datx aquari: C: F. F.
Plures esse casus possune; ut nempe punctum L sit intra Semicireu-
lum C:C F (idque positum inter punsta C, C, vel inter ipla C, F) vel
in altero Semicirculo OF F, ulera C P lito respectu puncti C; sed
haec una construstio simul ac demonstratio parirer omnibus convenit;
ut pluribus huc nOn (IE OpUS.
VII. Adnoretur saltem quoad istos casus, quod sicuti per punctum
C (ut antea comostratum, aliquando quatuor rectae duci postune
datam adae quantes, rectisque FC, FV terminatae; binx scilicer inter
angulum quo punctum C continetur, alterx que toridem extra iptum;
nonnunquam vero eres solae; quum data recta minima conrinset este
cunctarum, quae dicto punctum C concinenti angulo portur interleri;
Tubinde tantum dux, quando data cali minimae cedit; ita respectire
Problema jam expolitum plures totidem soluriones accixir. Sane
quomajor esthic data Z, eo minor eradet intercepta RS; e vicissim
quo minor RS, eomajoripsa IZ; unde (sEuerit LS omnium mini-
ma, quae angulo C F. V punctum C: capienci inseri possunt, etiam VIL.
maxima eric e C prodeuntium rectarum, gux inter diatnerrum (F,
e Semicirculum OF. F comprehendi pollunt. unde Porismatis loco patet,
e supradictis, quo pacto talis maxima duci poltit; de hoc ipsum Pro.
blema penitus dererminari. quod accendenei non obscurum innuisse
Facis videtur. jam ad principalis quaeliti relolutionem accedimus; ita
jam breritur propotiti.
VIII. Per datum punctum X rectam ducere, cujus retexus datae
Polirione recta B C Sic parallelus.
Id sic eticitur. Centro X per C describatur circulus OL F C;
itemm per Z ducatur C F ad BC parallela; tum ex C prioiciatur
recta cujus secundum Lemma mox praecedens, intercepta pars H L.
requetur demidiamerro rehectentis circuli; quae e illum secet in H;
ductae
ic
73374.
F18. 73,740