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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 69, page id 1041163592:0103
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PRTNCIBTA MATHEMATICA.
vercetur in geminas Rectas, quarum una est recta illa in quam pun-
ctum p incidie, ec alcera est recta qua alia duo ex punetis quatuor jun-
Suneur. Si Traperii anguli duo oppoliti simul sumpei aequentur
duobus rectis, e lincae quatuor P ∞, P R, PS, PT ducantur ad
latera ejus vel perpendiculariter vel in angulis quibulris aequalibus,
Scque rectangulum sub duabus ductis P  X P R aequale rectangu-
10 sub duabus aliis P SZ PT, Sectio conica eradet Circulus. Idem
Ret si lincae quatuor ducantur in angulis quibulris ec rectangulum
sub duabus ductis P aX P R Sic ad rectangulum sub aliis duabus
PSX P T uc rectangulum sub sinubus angulorum S, T, in quibus
duae ultimae PS, P F ducuntur, ad rectangulum sub sinubus ansu-
lorum Q R, in quibus duxe primx P 4 P R ducuntur. C aeteris
in calibus Locus puncti F erit aliqua erium fsurarum quae vulgo
nominantur Sectiones Conicae. Vice autem Trapezii ABC. D sub-
icui Potest Ouadrilarerum cujus latera duo oppolita sC mutuo in-
Har diagonalium decusant. Sed et c punctis quatuor A, B, C, D
Pottune unum vel duo abire ad intinitum, eoque pacto latera h-
Surx quae ad puncta illa convergune, cradere parallela: quo in
casu sectio Conica transibis per caerera puncta, ec in plasas paralle.
larum abibie in intnIcum.
L E NI N A ZIX.
Invenire punctuP, a quo si rectae
quatuor PO PR, PS, PT,
ad alias totidem positione da.
tas rectas AB, CD, AC, BD,
sinculae ad singulas in datis
anculis ducantur, rectangulu
sub duabus ductis, PO XPR.
sit ad rectanculum sub aliis
duabus, PSX P I, in datara
tione.
Lincxe AB, CD, ad quas rectae duxe P Q F R, unum rctan-
gulorum continentes ducuntur, conveniane cum aliis duabus posi.
tione dacis lineis in punctis 1, B, C, D. Ab eorum aliquo  agC
rectam quamlibee FF, in qua relis punctum P reperiri. SCcCL Ca
linCaS OpPOScaS B D, C D, nimirum B D in HI ec C D in F, ec 0b
lacos omnes angulos Fisuraes dabuneur rarioned P Q 2d F A e P 
2C
ea
LIBEK
PKINVS.