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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)
# Folio 393, page id 851387705:0413
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FLN LTOR UM
P R O P. L.X.
Corollarium.
ROO, Conocidea es Pyramidoeidea Parabolica C Paraboloeidica; quae
nempe Parabolae, Paraboloeidi cubicali, biquadraticali, supersolidali
Oc. aptantur; sunt ad Cylindrum es prisma circumscriptum, (vel
aliud quodvis super aequali base aeque altum,) ut 2 ad 4, 3 ad 5, 4 ad 6.
5 ad 7, 66.
Cum enim Parabolae, de Parabolocidium illorum plana sine series rectarum in
ratione subsecundanorum, subtertianorum, subguartanorum, TubquinFanOTUM, _C.
sire uc radices quadratiex, cubicae, biquadraticae, supersolida, dec. Primanorum:
Conocidea e Pyramidocidea sic aptata, sunc series planorum in duplicata ratione
iltarum rectarum; et propterea, uc radices quadratieae, cubiea, biquadraticae, su-
persolica, ec. Secundanorum: quibus in rabella altignancurrationes illae 2 ad 4.
3 2d5, 4 ad 6, 5 2d 7, ec.
e ROP. LXI.
Corollarium.
CFd C hinc innotescit methodus quadrandi non modo Parabolam sed 5
Paraboloeidea omnia, (eorumque complementa,) non modo ea quorum
ordinatim applicatae procedunt juxta rationem simplicis alicujus potestatis,
(de quibus dictum est prop. 55, 56, 57, item prop. 23, 45.) Sed es juxta
rationem potestatis cujussis ex simplicibus compositae. Puta: si ordinarim-
applicatae sint in diametrorum ratione duplicatae subtripticata subquintupti-
cata, subseptuplicata, eSc. vel triplicatae subquadruplicata, subquintuplicata–
C3c. rationem habebunt ad Paralleloerammum circumseriprum eam quam ha-
vent 3 ad 5, 5 ad 7, 7 ad 9, 530. 4 ad 7, 5 ad 8, 3c. Et eorum com-
plementa (quorum ordinatim applicatae erunt propterea un suarum diametro-
rum ratione subduplicatae tripticata, quintuplicata, septuplicata, (3c. item
subtriplicatae quadruplicata quintuplicata eSc.) rationem babebunt 2 ad 5.
2 ad 7, 2 ad 9, (30. 3 ad 2, 3 ad 8, 3c. Eit similiter in caeteris: junta
tenorem praecedentis Tabellae, prop. 59.
Nam si ordinatim applicata sine in diametrorum luarum ratione duxlieae
subtriplicara, erit planum illud series rectarum qua se habent ad invicem ut qua-
drata radicum cubicarum, (vel ractices cubiex quadratorum) numerOrum Aricti
metice proportionalium, sive ut radices cubica secundanorum; quibus in Fabell
convenit ratio 3 2d5.
Ec hujus complementum ordinatim applicatas habebie in diametrorum suarum
ratione lubduplicatae criplicata, (quod cali arsumenio probabitur, quo utus sum
ad PrOP. 23.) de propterea planum illud erit series radticum quadraricarum Cy.
borum lire Pertianorum; quibus altignacur in Tabella ratio 2ad5
Et pariter de aliis judicandum.
SC TIOZ LM.
Atque hoc pacto alix adhue trourx currilinea (praeter eas quas innuimus ad
PrOP. 45, e 57.) ad aequales rectuineas reducuntur. Nempe onnia cujuleun.
que generis Pacabolocidea, et eorum complementa.
ACF.