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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 229, page id 175905688X:0251
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AI
1C
e
COMMENZAREE EN LEDRAMII.
erit b-
2.2)
 - = 7. A deo que si addantur perpendiculares inventa
E. F, EG, _ FHI, eric earum lumma b, aequalisb, perpendicu-
locrianguli ABC.
EIbi patec, quod, postquam incidimus in xequationem, in qua
ab utraque parte repericur eadem quantitas, quaeltio propolica
non sic Problema, Led Theorema; leu quod conditio, ex qua
haec aequatio deducta fuic, in quaeltionis datis sic comprehenta.
neque unquam line hac conditione esse portit: Atque adeo.
duas in ea conditiones desiderari, ad dicti puncti determinatio-
nem; unam, ad aequationem prox inveniendam, ou d innocescat,
2d quod punctum linex A C duci debet perpendicularis F F; at-
que alteram, ad aequationem pro rinveniendum, qua cornolca
cur, abinam illud ipsum in hac perpendiculari sit lumendum: qui-
busmediantibus quaectio penitus determinata reddatur. OuarC, Vide ea, quae
Poltquam conditiones in quaeltione praltandae exlecuta lune, de habentur
neueri linearum incognitarum AF, FF. aequatio respondet, po- paz. 4.
terum illa ad arbierium accipi, atque idcirco quae licum punctum
F. ubique inera criangulum AB C allumi. Cujus demonstracio
Facilis est.
Ducantur enim reCtX AF, F B, X F. C, ut constituantur eria
triangula AF C, AEB, XBF C.
Ouoniam igitur horum triangulorum bales lunt aequales, ac
quaelibet ex iplis aequalis basi trianguli A B C; habebune ipla ad
triangulum AB C eandem rationem, quam perpendicula FF.
EC,de L FI. Ouare cum criangula AE C, AEB, _ B F. C Cinul
sumpea ipsi criansulo AB C sint aequalia: crune quoque perpen-
diculares F F, FC, _ F HI sunul sumpex ipsi perpendiculari BD
aequales. Quod etat demonstrandum.
Porronotandum est, quod, quemadmodum punctum C, intra
triangulum AB C alsumprum; exhibet semper candem Cummam
perpendicularium P F, FC, _ FHI, guxe ab eo ad trianguli late-
ra deducuntur, ee aequalem perpendiculari BD, ita contra, si Tu-
matur extra triangulum AB C, atque ab eo ad finsula ejus latera,
si opus est, producta perpendiculares demittantur, obtineatur
lemper eadem perpendicularium differentia, quae rurtus perpen-
diculari BD sic aequalis. Oportet aurem perpendicularem, qua
ducitur in lacus subrenlum angulo, incra quem punctum sumpeum
CTIE