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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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At.
LALENITORUM
PROP. XXXIV.
Corollarium.
T universalicer, Ductis quotlibet rectis MIT, MT, Cc. anculos conti-
nuos PNTT, TATT, C30. aequales invicem facientibus; fieurae Spirales
continuae, his rectis interpositae sunt ad invicem, ut F, 7, 29, 37, 6+, (3c.
Nam (per DTOB. 30.) Lisura Spirales à principio ad has lineas continuatae funt
UE F, 8, 27, 64, 225, eC. Ergo Fisura inricem continue sequentes his rectis ter-
MInaLA LIINE NE F, 8 - + =
17, 27 - 8 = 19, 64 - 27 = 37, 225 - 64 = 61. _cc.
Yct ut 367 367 3 67367 569 etc.
P R OP. XXXV.
Corollarium.
Enique Fieurae Spiralis portiones, quae in simeutis circulationibus de
novo describuntur; (praeter illud quod in praecedente circulatione de
scriprum fuerat, nempe, quod intra Spiralem primam continetur, quod inter
primam cd secundam, quod inter secundam e tertiam, quod inter tertiam es
quartam, edc. sunt ad invicem ut F, 6, +2, +8, 24, ec. (addendo semper,
post locum secundum, numerum senarium;) Nempe ut differentiae disseren-
riarum numerorum cubicorum.
Sequitur ex 33. Guia 17 7 = 2, 19 = 7, 37 = +9, 62 - 37, dc. TuNE 1
2, 67 12, 18, 24, c.
SC FIOL ZV MI.
Flaec aurem de area Figurae Spiralis doctrina, concinuis duodecim propolitioni.
bus jam cradua, consona est illis quae tracic Archimecdes cirea tinem libri de Li-
neis spiralibus. Labet aurem id iplum paulo ulcerius prosequi.
PROP. XXXVI.
Corollarium.
omplementum feurae Spiralis (quod nempe cum ipsa sectorem contermi-
num complet) est ad sectorem conterminum, ut 2 ad 3.
Sequicur hoc quidem ex prOP. 24. Sed id iptum alicer ostendemus hoc
modo.
Constare supponamus FBuram PMI T J (complementum Figurae spiralis NI L LM)
ex intinicis numero accubus PP, PY, esc. qui quidem lune in duplicata La
tione rectarum MP, MP, Arichmetice proporcio.
nalium, (uc ostendimus ad prOP. FF.) sector au-
tem conterminus MP F, ex tocidem constabit ar-
cubus, ipsis MP, MP, proportionalibus, adeoque
Arichmerice proportionalibus, (ut Datet:)
EsE autem series ejusmodi, (in duplicata ra-
tione Prichmerice proportionatium,) 5 leriei aequa-
lium, (per proP. 21.) d Series Rrichmetice PrO-
portionalium : ejusdem feriei aequalium, ( per
DFOD. 2.) Erso illa ad hanc (hoc cst, comple
mencum tigurx Spiralis ad Sectorem) ut 3 ad 2,
hoc CAt, ut 2 ad 3.
PROP.