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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
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NFINETORUH
alem omicta Spirali linea gennina, spuriam hanc Spiralem Deripheriae compata
verim; causa elt, quod huic possim, non aurem illi, aequalem peripheriam altignare.
PROP. XIV.
Corollarium.
PPropterea etiam Segmenta Spiralis hujusmodi, a principio Spiralis
exorsa sunt ad rectas conterminas, sieut P’arabolae Diametri interceptae
ad ordinatim applicatas.
Nempe in ratione duplieata, pex PrOp. 1F.
PROP. XV
Coroll.
Deo si supponatur Spiralis nostra N T F ita
evolvi ut rectam constituat, es rectae omnes
TM TM, fiant invicem parallelae; erit illa
Diameter, hae vero, ordinatim applicatae in Pa
rabola: Contra vero, si supponatur Parabolae dia
meter ita in arcus convoluta ut ordinatim-ab-
plicatae ad idem punctum terminentur; fiet illam
Spiratis: ista, rectae conterminae; hoc denique,
princixium Spiralis.
SC ZIO F. ZV M.
atque hinc eriam ulterius pacet illud quod PosL prOP. L3. indicarimus. Nempe.
Soiralem illam nostram ex intinicis similium Sectorum arcubus contlatam, non esse
senuinam spiralem proprie dictam, sed ipla minorem. Cum enim constet, in Pa-
rabola, ordinatim applicatas, quae rercici propiores sunt quam ea quae lateri recto
aequatur, lonsiores esse quam sune diametri interceptae; adeoque non ita convolvi
DOsC Parabola diamecrum (dummodo infracta maneat) uc earum ordinatim appli-
catarum extremitares in ipso rertice cocan, (quippe quodque qua jam currata lup-
ponitur, minor esse non poltic, quam recta contermina, qua priuscrac ordinatim
axplicata:) Necesse est ut rera Spiralis, qua sic conroluta elt, major sic quam
ea qua supponitur ex arcuum aggregaro conttari, quam Pgrabola diametro con-
venire jam oltentum elt quippe quae est ubique in duplicata ratione rectarum con-
terminarum.
P R O P. ZVT.
Corollarium.
rabola vero si convotura (hoc est, fieura Spirati nostrae adjacens) est
ejusdem Parabolae evolutae semissis.
Frenim r. 8. Si Supponamus paralletogrammi P MLatIS P P ita CONVOHL UE re-
ctarum omnium PM puncta M in eodem puncto coc-
ane, tiet ex Parallelosrammo (proprer radios omnes;
communi centro M aequales) circuli sector (qui circulo
inteoro vel minor eric vel major rel aequalis, Pro Ca
rarione quam ad invicem habeant rectae PP, PM:) qui
quidem Sector (hoc est Paralleloorammum convolucum)
erit Parallelosrammi (eroluri) Semistis; (Propterea
quod pro intinitis Parallelorrammis ex quibus P’arallelo.
Srammum expolitum constare suxponitur, tiune coridem
in Sectore criangula easdem ee bales e alcicudines ha
beneia:) Pari modo, si ica conrolratur Parabola ut dielum cl, ut ordinarim-
appliediarum (pridem parallelacum) caciema altera in eodem puncto cocaliu,
A2a 2
PxOD.XIV
intinita