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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 90, page id 1041163592:0124
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90
PETILOSOPMLSE NATORALIS
Deors culum certium F. M F in c. FE compleatur Figura ABC def simi-
Conronon lis e aequalis Fisurx abcD F. F. Dico Factum.
Agatur enim FC ip(I a D Occurrens in n, de jungantUr a CF, bG
C,8D, DD. En constructione est angulus F. a D aequalisan
DuloC LB, de angulus
ac F aequalis angulo
ACB, adeoque crian-
oulum anc criangulo
ABC aequiangulum.
Froo anoulus anc seu
Fn D angulo ABC,
adeoque angulo Fb D
requalis CA; ex PrOPtCF-
ea punctum n incidicin
punctum b. POrrOan-
sulus CP ∞ qui di-
midius est anguli ad
centrum ( F D, aequa-
lis est angulo ad cir-
cumterentiam ( a D;
dc angulus C QF, qui
dimidius est anguli ad
centrum (QD, X
qualis est complemen-
+0 ad duos rectos an
ruli ad circumterenti
a Gb D, adeoque x
qualis angulo CFba3
funtque ideo triangu
la P Q Gab simi-
lia; et Ca cA ad ab
UE GF ad F Q; id es
ex constructione) ut
Ca 2d AB. A. Quan-
tux itaque ab _c AB; e propicica ngula abc, ABC, quxe mo-
do similia esse probarimus, sunc eriam aequalia. Onde, cum tan-
sant insuper trianguli D P. F anguli D, L, Fcrianguli abc latora
ab. ac, bc respectire, compleri porest Figura ABC d et Fisurx
abcD P Fsimilis ec aequalis, atque eam complendo solvetur Pro-
blema. 8. F. F.
COr010