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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
# Folio 53, page id 824573315:0265
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PFOD. 65.
Aritheretica Insinitorum.
rum radicions quadearicis,) 2 ad 17, lire 5 ad =Z hoccA 1 ad
2F 1. (K. FliC de exreris.) Quod attirmae Theorema. Sin Index
supponacur irracionalis, puca N 3; eric ralio, uc 1 ad a F V 3. _C.
PROP. LXV.
Theoremao
X cognitaratione quam habet qualibet scries ad
seriem Aqualium, coenolcitur racio quam HaLCC
quaelibet ad quamlibet allam.
Ensempligracia. Parabola ad crianeulum, (hoc e Te
sublecundanorum ad seriem primanorum,) uc 3 ad = vel uc 4
ad 3. Semi parabola complemencum ad Triangulum, vel ccia
Conus au Conoides Parabolieum, (hoc est series secundunorum
ad leriem primanorum,) uc 3 ad 2, vel uc 2 ad 3. Semi- parabo-
la ad Cuum complementum, Choc est Ccries sublccundanorum
ad Teriem (ccundtanorum,) uc 5 act 3, vel uc 2 ad F. Sic Parabo.
la 2d paraboloides cubicale, ut 3 4d Z, vel ut 8 ad9: Fc C0-
noides illius ad Conoides hujus, ur Z ad 3, vel uc5 ad6. Para-
boloides cubicale ad Biquadraricale, uc Z 2d 3, rel uc 15 ac
16: Fr C onoides illius ad conoides hujuss, uc Z ad Z vel ut 9, ad
1O. FCHC in aliIS.
Incelligc; Li casdem vel xequalee habeane ee bales de alcicudines
auclalcem reciprocatas:) Nam si direrlas habeant vel bales vel
alcicudines vel ucragne, racio ferici unius ad aliam, componi-
cur ex rationibus e balium et alcicudinum et ea quae el lerierum
provria. Pura B Parabolae balis B
alcicodo A, Frianguls basis e alcirudo
a; erit parabola illa ad Petangulum,
ut 3 A B ad 3 a6, vel 4 A B 2d 3 a6
ee paricer in caeceris. lem, si Peiangu
li basisB, alcicudo A; e ParabOI~
batisB, alcimdo a, erie Parabola ad
Priangulum uc E a B ac = AB, vel
4 aB 2d Z AB.
Demonstracio paret Cum enim Pa-
rabola AB sic ? Paralleloerammi A B,
_ Triangulum a C. E P rallelocramam
a6 ericilta ad hOC UL 3 A B ad 2a6.
he limilicer atiis