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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 41, page id 797435492:0073
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V E C F. V.
eric.  Sin punctum T extra datum angulum exictat, evidens est ran
cum uno modo problemari lacistactum iri; quodque per alceram in-
ersectionem, e Y, ducca recta ad angulum pertinet dato verricalem.
hiaec, inquam, tantillium actendenti manifeste constabune; nihil ut CIE
opus hic plura verba consumere. verum ut in horum caluum primo
constet (id quod pro sequentibus ex usu erit cognoscere) quando
dictus circulus hrperbolem continoit; seu quando tantum una per
Y recta quancicaris ejuldem incerseri poltir, hoc adrectemus Thco-
rema.
IX. Si a puncto quovis Y intra rectum angulum X P F existente F18. 54.
demitrantur ad ejusdem anguli lacera perpendiculares YB, YD; ac
inter YB, YD proportione medix sInE reCtX BH, GD; Per pUnCta
N, E, Co cranlibit recra cunctarum minima, quae per Y ducex ansu
lum X P F subrendere posune.
Ouod HYO CIEuna recta patet, quoniam est YB. BH:: GD.
D Y (ex constructione nimirum) porro per P eranseat alia quxcunque
reCT L YM; _ N Had C N, M H ad P F perpendiculares concur-
rant in HI. item HI A ad NVC parallela ducarur; _ C S ad P F
denuóque connectatur GHI. Jam pacettriangula CDY, YBH;
HIMN, AIM _ Cimilia Fore; quodque proprerea est MH. MR::
MNg. MHq:: DCg. YDg. irem (ob BH, DC, YD..
eABH. YD:: DCg. YDg. hoc est YN. YC (vel MNI. 6S)
:: D6g. YDg. ergo eAt MN. MR:: MN. CS. adeoque M H
=65. itaque major eAt CS ipsa M T; abeoquerCCEX OHI, L. M
PTOTTACEX COnCurreNE; puta ad Z. ergo LM. GH: : LZ. 62.
rerum proxter angulum L G HI recro P majorem, cA L. L. L 62.
quareL ML GHI. ast ob angulum rectum C NH eA CHIC ON.
quare magis est LM E CN. codemque modo quaeris per P ducta
major ostendetur ipsa OH: Q. F. D.
Z. Ilinc etiam Si C N sic in ratione T B ad Y N quarca proxortio-
nalis; erit C NI minima. nam inde consequetur Fore YB, BN, GD,
YD -:. Frenim erit TNg. YBg:: GN. YN. _ dividendo
BNg. YB9:: GY. YN:: DY. BH. ac inde ZBGKDY =
BNcub; velDY=
BNI cub
tione YB ad BN.
B9. IEaque D Y est quarca proportionalis in ra.
ate ant F  Anceo hetudt.A Edtat
rioribus