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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 407, page id 851387705:0427
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Pr
NFINITORUM
DB. EEd AxdB-
: dAX L AXDB. D A9XDB::
I
DB. FHEOEEDALDB. dA Xde
D A.
Corollarium.
T vero feura plana (AD BB) sit ex serie rectarum Tertianis recipro-
Dlarum constata; (quae nempe sint rectis complementi Paraboloeidis cubi-
calis ADB, Co Paralleloeramimi ADF, tertiae proportionales;) erunt rectae
illae (DB, aB, Cc.) in reciprocae rationis Diametrorum (D A, d A, (3c. )
ratione triplicata (scil. ut d AC, D AC, CdC.) Ft Paralleloeramma inscripta
ADB, AdB, BC.) in reciprocae rationis diametrorum ratione duplicatam (si
ut d 9,D A9, C3c.)
dB =
Fst enim (ex constructione) DB. dB:: dB. DB:: d AC. DAC. EL propterea
etiam dB =
aB=
dAE DB. ErgO ParaHLelOBTamma ADB. AdB: : D AX DB. d AX
d A XD AC
EDB-
DA
d
Ouod crac demonstrandum.
=DB:: d A gx D Ax DB. DA CxDB:: d A g. D A g.
5C 77OZ ZV M.
Arque eodem modo de aliis ejusmodi sixuris planis ex qualibet rectarum serie
reciproca conttacis judicandum erit; ut de de Parallelogrammis (sire rectangulis
sire obliquangulis, prout sicus figurae poltulat,) ipsis inscripris.
Ouod ad Aream aurem accinet iltarum tigurarum ex seriebus reciprocis con-
Ctancium; quarenda est illa eodem fere modo quo lupra in seriebus directis. Vbi
aurem series directae indices habent +, 2, 3, _Cc. ut quae supra seriem A qualium
ioc gradibus ascendune; habebum hae quidem (illis reciprocae) suos indices con-
ErarIOS negaLIVOS = L, = 2, -3, ecc. tanquam cor gradibus intra seriem A. qua
lium descendentes. Proutaurem illae ab o ciptra rel Wihilo continuo crescune, bixe
contra ab ∞x Intinito continue decrelcune; acque ut illic terminusmaximus, hie
minimus, seriem claudit: (qua tamen et pro arbirrio concinuanda supponitur,
quousque libet illic crescendo, hie decrescendo.) Adeoque, ur illie tigura Cir.
cum (cripta (parallelosrammum puta vel prilma) sire series toridem terminorum
Maximo aequalium; hic, tigura Inscripca, sive series cocidem cerminorum Minimo
aequalium, habenda est pro communi mentura ad quam facienda est comparatio;
urrobique ad illum terminum respectu habiro qui leriem elaudit.
Neque incerim mirum cuiquam videatur (ut uc Fortalsis in exspectarum,) si t.
Bura interminatae rationem ad datam aliam terminatam inquiram. Ouamvie
enim hujulmodi sgurx ADB (uc uE ex parte DB ad libitum cerminaca, ut
modo in his scholiis dictum est,) SuPPOnANEUT ex Parte SB in infinitum conti
RUATA (PEF PFOP. OZ.) nOn tamen propterea vel nullam vel semper intinican
rationem habicura sunc ad datam fguram terminatam, puta ad parallelogrammum
aque altum super eadem bali DB descriprum. Quod eo quidem facilius allen
tum obtinere posse videatur, cum id iptum in una quactam tigura solida (quam
Eyperbelicam accucam infinitam rocat) jam ollenderis Forricellius sed neque
seriper