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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)
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PrOD. 192
rithmetica instnitorum.
tum sic numerum incegruns sine ulla adjuveta Fractione jute
minore esse, Fractio prima, huc incegro adjuncta, quancitatem
augec: led cominus aueer quo ipta minor lueric. HaC isITUIE
Deima Fractio quancicarem auger, e quidem eou lq; VE jam, 9112
Fuerac justa minor hac justa major. Hlujus aucem tractionis, co
dem MAMENCEnUmeraEOrE, LI denOMINaEOF AUSCaTUE, (quod HC
adjecta tractione Cecunca.) Fractio prima, adeoq; _ EOtA quan-
ticas, adjectione secundae minuirur. Baec aucem diminutio co
minor erit (adcoq; e coca quancicas major) quo ipliusle
cundae Fractionis (manence numeracore) denominator ause-
cur; quod sr adjectione certiae Fractionis. Tercia isitur tractio
secundum minuic, adeoq: primam auset, uc d toram isicur
quancicacem. Fx similicer in sequentibus. Puca guarrae adjectio
minuie certiam, hoc est, auger, secundam, adeoq; minuic pri
mam, cocamqi quantitarem. Ouinca minuie quarcam, adc09
auseecerciam, minuic secundum, angecq; primam coramq;
quancicarem. Adcog. Fractionum adjectio in locis imparibuo
augec, in paribus minuie quantiearem: Ouod non de his can-
cum, led de quibulris aliis Fractionibus ica (quoad denominacon
res) concinue Fractis, incelligendum erie.
Acqi hactenus Nobilissimi Viri mencem, quanta pocui brevi-
tace simul acq; perspicuitate expolui; quaeq; de iptius methodo
dicenda habuibrericor indicari.
PROP. CZCII. Theorema.
CTEc aequabilis Curra (non hinc inde (uBsuITanS) VC,
cujus Axis VX, e Tangens invertice VI; unde
ductis ad curvam rectis axi parallelis, ex ab invicem
aequalibus distantiis remotis, harum Sccunda, Ouar-
ta, Sexta, Octava, _c. ( in locis paribus,) sint ut
1,6930, 140, _C. (qui numeritiunt ex concinus mul.
ciplicatione horum, IXE + 287 24 , =2 _C.) Erit, ut SC
cunda adT ertiam (hoc cA, ut E ad numerum ipsIS 13
o incerponendum.) sic Semicirculus ad Guadratum
Diametri.
SequiCUE CX PrOP 139, CF 135.