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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 40, page id 797435492:0068
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E18. 5T.
E18. 5
l. E C F.
tum _ levi pede praetereo; quoniam aliunde MOX ApParitUEA) CIt
inguam, ejulmodi qualibet interlectio N; dico Fore X N, iplius AN
retractum. Ficenim est I. R :: AH. A T. hoc est (quoniam AHI,
KX Tunt ex Constructione pares) I. R:: KZ. AT:: NR. N A.
unde maniteltum, e praemonstratis, est proxolitum.
VII. Veruntamen hujusnodi constructiones Geometrarum ulus
aut non libenter admittit, aut alias saltem exigir per lineas vulgono-
cas, atque receptas; itaque consuetudini morem serentes rem aliter
conficiemus. huc ucique Faciens sequens Problema Lemmaticum pEX-
mittentes: Dato angulo rectoZPF; punctóque quovis Y; per hoc
rectam duce: C dati anguli cruribus occurrentem, (c ut ab iis intercep.
ta lic aequalis datae rectae T. I Fxpecitissime quidem perticitur hoc ope
Conchordis alicujus polo Y delcriptx; sed enim quoniam ex ilte modus
handica Ceometricus censetur: adhuc iildem Cicometris obsequentes
ita provolitum exequemur. Ducatur Y B ad P F perpendicularis; e
symprotis PX, P B ducatur Ryperbola per Y transiens (( quidem
punctum Y existar extra angulum datum, aut iltius oppolira (sc. pun-
etum P(ic intra dictum angulum) cum centro Y interrallo daram Y
aequante descriptus circulus sipperbolam inteerlecet in R; _ a K de-
MItTatUE K L ad B P perpendicularis; accipiatur aurem BBI = - PL:
ec per H Y crajiciatur recta N. C. dicotactum; vel esse NC parem
datxe T. 1) Nam (ducta PHI adP B Parallela) ex Hyperbolae prorrie
tate est lL x LR = P BX BP. adeoque cum lu ex constructione
BVI = PL: eriE BNXL K:: P BXBY. adeoque BNI. BY::
PB. LK. est autem BN. BY:: DY. DC. eroo est PB. I R::
DZ. DC. quare cum (IF P B =DV, CRIEL R = DC. adeoque
(pares L. HI, D P addendo, vel Cubtrahendo) est REI = CF. quin-
eriam est ZHI = I B = P N (communem nempe P B, vel L P
addendo) Ergo patet Fore YK (vel T) aequalem ipliCH: (. F. F.
VTII. NTocandum est aurem in catu, quando punctum Y intra darum
angulum XP F existic, quod circulus ille centro Y descriptus lubinde
delionatam hyperbolem binis punctis secabit (quod enim pluribus haud
quoquam secabit univertum haud ica pridem circa tales ad eadem con-
vexas curras octendimus) quo casu putet duas obvenire proxosiri solu-
tiones, alignando rursus ille dictus circulus FEyperbolen continget. et
cum una tantum per Y duci poterit recta, datam T adxquans; illa
scilicet omnium gux per Z daco angulo incerleri possunt minima.
Duodsi cirenlus Hyperbolx non occurrat, Problema prorsus  eisor
exit