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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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ceruorum Descensis
Aia Demonstracio.
eap. 11
Pocest hoc idem demonstrari, ex PrOP. 2F. proxrer Obli.
quiorem alibi Descentum: hoc modo.
In Decliris Plani P GOHI puncto C, consticurum inceli
satur Grare: Acque, in eodem plano, cum ITorizoncalis
recta PC (nempe ea recta lecundum quam Hlorizontale
Planum, Der C trantiens lecat Declire planum,) cum huic
ad angulos rectos GO: Tnoeque ad lubjectum Planum Llori-
zontale FOR, demilta pervendicularis GR: (Per quam
itaque, nili impediatur, delcendet Grare; per 22 hujus.)
Incelligatur aurem, ob duririem Decliri Plano subjectam,
impediri ne Denetret. Dico per CO descenturum Grare.
Cum enim duo Plana Forizoncalia, adeoque Parallela, alcerum in FLO, alte-
rum in PC, secer idem declire planum P CiOHL (per constructionem:) CxUNE
HO, PG, Parallelae rectae. per 16 Flem. FF.
Tiem, propter DC rectam, rectis GO, GR, ad angulos rectos, (per constructio.
nem,) erit ad planum OCR recta, (per 4 L. leM. TT.) Adeoque et (truie paral-
dela) HO, eidem OGR plano recta exiu (per d L lem. L1.) rectiique OG, OR,
ad angulos rectos; per 3 Det. F LCM. EF.
FE, sI GentrO R in plano HOR, ducatur per O, peripheria OS; eam con-
tingens TIO, extra peripheriam jacebit; per 16 Flem. 3.
Si iraque ad recta LIC, aliud quam O, punctum quodvis T, dueatur C Y re
Etaque _ R I jungatur; secabit haec peripheriam; Puta in S. Fec, juneta CFS, erit
(proprer CR ad planum Horixontale rectam; adeoque angulos GRO, (R5.
aequales rectos; _ RO; RS, aequales radios; rectamque CrR communem) SG
recta, aequalis rectae OC; et angutus S EF R aequalis ansulo OGR; per 4 F. lem. 7.
Fst aicem angulus PER, major angulo SGFR (parce Cui,) ergo ee (huic
aquali) angulo OGR major elt. Adeoque Descentus obliquior eMt Per GT,
quam Der (O.
Cum igitur Cirare, quam porest recta ad Cenirum descendat, (Per 2 F hujuS ;)
Per GO potius quam CTP FeretuIT.
Arque similicer de aliis ejusdem Plani rectis ostendetur. Adeoque d Forciori, de
rectis ulera planum, auc etiam curris.
deoque (cum nec Planum penetrare posTiE) per rectam CEO (nisi alias impe-
dicum) descender Grare in C, (ue qui reliquis rectior elt Descentus:) Ouod erac
demonltrandum.
SCHOL. ZOM.
FAnc Demonsteationem praecedemi subjungere vitum ell, propter ea quae apud
a Mechanicorum Scripiores de Obliquitate Delcentuum Occurrunt, Anguti-
que Obliquitaris magnicudine. Ac priorem ego praetulerim, quae ex Dectiritate,
hoc e ex Alcicudne rectarum lonsicudine aqualium, vel Longiudine aeque
altarum, depender: cum uc simpliciorem; cum praecipue, quoniam quod ex Obli-
quicare hac oritur Cravicationis impedtimentum, Ausmenco lonsicudinis Descen-
luum aeque:
jam dictis _e post dicendis manisestum eric:) Adeoque illi Borius, quam huie, ut
vera caula referendum.
Hinc aurem seguiur; Fandem esse Descensus Cravis in Declivi Plano, iptius.
que Dectiris Plani, ad Florizoncem Tnelinarionem; (Nam, Per DeF. 5 et 6, L lem. LL.
Ansulus GOR est Inclinarionis Mentura, cum recta GO, cum plani PCO, ad
Horirontem HIOR:) Adcoque eandem utriusque tam Obliquicarem, tam Decti-
vicarem. Nempe idem Obliquicacis Aneulus OCCR; cademque Decliricas sive
rectae CO ad C R, ratio.
eROP.