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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 70, page id 1041163592:0104
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III. IIII
PHTLOSOPMLLE NATVRALIS
DE MorD ad Z S, adleoque ratio Z Q ad
GORROROM P S. AuFerendo hanCa dACaFZ-
EIONC PQX P R ad PSXPT.
dabitur racio F R ad F T, e
addendo datas rationes P I 24
PR, _ PT ad F E dabitur
ratio F F ad P BY acque adco
punctum P. Q. F. I.
Corol. Y. Flinc etiam ad LOci
punctorum infinitorum P pun-
ctum quodris D cangens duci
Pocest. Nam chorda P D ubi
puncta F ac D conreniune, hOC
est, ubi AII ducitur per punctum 
ultima ratio cranescencium YP SE F
isitur AD duc parallelam CF, occurrenem B D in F, sc in ca ul-
tima ratione sectam in F, _ D F tangens erie, propterca quod CF
e cranescens IFY Parallelae sune, ex in F ex P Amiliter secta.
Corol. 2. Tlinc etiam Locus punctorum omanium F detiniri potest.
Per quodris punctorum A, B, C, D, puca A, duc Loci tangentem
AF ec per aliud quodris punctum B duc tangenti parallelam BL
occurrentem Loco in F. Invenie.
cur autem punctum fper Lem. XIX.
Biseca BF in C, ec acta indehnita
AC erit politio diametri ad quam
BG_ FC ordinatim applicantur.
TIaeC AG occurrat Loco in II, e
erit ATI diameter sive latuS Fran(-
versum, ad quod latus rectum crie
ut BG9. ad C FI. Si AC nullibi
occurrit Loco, linca A exictente
infinita, LOcus crit Parabola ec l2
rum rectum ejus ad diametrum AC
B60
pertinens erit=
e
Sin ea alicubi occurrie, Locus FTyperbola erit
ubi puncta A e FY CTa sunE ad CaIdem pAFFCS ipSIUS G: ex FIIIPSIS,
ubi intermedium est, nis Forre angulus G B rectus sic ex insuper
BC quad. aequale rectansulo AGFI, quo in casu Circulus tabebitur.
AEqueica Problematis Veterum de quatuor lineis ab Luclide incex-
ei de ab Apollonio continuati non calculus, sed compositio Creometri
ca, qualem Veceres quaerebant, in hoc COrollario exhibetur.
LR N-
q
el ul Latc
CEUF UE CUPra. IpII