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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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Cap. L
DF CLDDSI
dissolvitur. De isieur ex dacis longicudine de lacicudine, (sive in Paralleloeram.
mo rectanoulo, live obliguansulo,) habetur arca mulciplicando: lic ex dala dlca
cum lonsicudine, habetur lacicudo; vel ex data area cum lacieudine, hrabetur lon
Situdo, diridendo. Acque de Parallelogrammis hactenus.
Cum aurem Ccodatiam jam lim asgreltis, hoc clt, mensurationem Planorum;
opera precium erit cuiam alia breVItI aCTExere qua eo Spectanc, ue cocum illud
plana menturandi negocium, Calcem prouc pexlencis insticuri racio postulat, ab-
solvam. Illud vero, quancum Cuperelt, menturatione Prianguli tere cocum per-
ticieur.
EIt aucem Friangulum (inceltise ficuram planam tribus rectis terminatam Mensurd
vel Rectansulum, cujus alter ansulus est rectus (nam plures esse recti non pol. sid Trian-
Tunc;) vel Obliquansulum, cujus omnes ansuli sunt obliqui: Hoc aucem, vel sul
Obcusanculum, cujus unus aliquis ansulus (quippe plures non polunt) obcusus
est; vel Acuranculum, cujus ansuli omnes sunt aculi.
AgorediaE PrimO, Priangulum Rectansulum. FIt autem omne Friangulum Frianeul
Rectanculum, Paralleloerammi Rectaneum dimidium. Si enim Parallelogrammum Rectan-
Rectangulum quodris (puca A D) diagonali linea (CB)
sececur, dividitur illud in duo crianguta (ABC, BCD,)
UE PaEE; quorum ucrumque elt Rectanoutum, (propter
ansulos ad A e D rectos;) sed ee invicem aequalia,
(Propter angulos aequales rectos ad A de B, e latera rC-
spectire aequalia;) de prourea ucrumlibet parallelogram
mi dimidium. Ec concra, Si Friangulum Rectangulum
quodibet (puta A B C) duplicetur ia nempe ut latera
Sll.
secundi cirea angulum rectum line homolosis lateribus prioris parallela, de latus
reliquum urique criansulo commune, tiet rectangulum paralleloerammum. S
enim sumatur lacus C D aequale ee parallelum lacerr AB, e similiter BD laceri
AC, (quae proprerea convenient in angulo recto ad D,) habebitur crians a
expolico simile de aquale, complens parallelogrammum rectangulum.
Flis politis; cum ex jam dictis innoceseat area parallelogrammi A D, innocelcee
etiam area crianguli ABC, quod nempe istius elt dimidium. PH autem arca
Parallelosrammi AD, quancicas producta ex ductu laceris AB in AC, puta AC
x AB; adeoque area crianguli (quippe illius SemitsiS) E AC X AB. Vel, li al.
ticudo AC. dicatur A, ec Batis AB dicatur B, erir area Parallelosrammi AB, area
Frianguli = AB. Ideogne
In Trianeulo Rectaneulo, si laterum circa anculum rectum, du.
catur alterum in alterius dimidium, emersit area Friansuli. Cuippe
dimidium area parallelosrammi. Atque hinc quidem ex datis tri
ansuli rectansuli lateribus circa anculum rectum constituris (qua
rum alcerum Batiu, alcerum Alcicudinem extribet,) mulsipticando coenoscitur ejus-
dem area.
Conra verO; Fx cognitis area e laterum eorum uno, innote seit
alcerum, dividendo. Nempe, si duplum arcae (AB) per alcicudi
A) AB (B
nem diridatur, habetur Balis; sin per batin, habetur alcicudo. B) AB (A
Puta A) AB (B. B) AB (A. Acque de Priangulo Rectangulo
tractenus.
a Frianguli Rectanguli calculo dependet. Demicta enim ab ansulo quoris in la- Obl1.
tus oppositum perpendiculari emergunt duo Priangula Rectangula; ex quorum quaneuli
caleulo cognoseitur area Prianguli expolici.. Exempli
Gracia, In triangulo BBC, ab ansulo C demilta perpen-
diculari C A, (unde tinne ad A anguli ucrinque recti
emergun criangula rectansula C AB, C AB. Si isitur
Ci A dicatuT A, AB dicacur b, AB dicatur B, e BB dica
cur B = b F B: erit (per modo demonttrata) = Ab arca
crianguli C A B, ZAB area crianguli C AB, ideoque
AB +
Hoc elt.
AB = = A B area torius CBB = C AB + C AB.
Trrsuli Obliquansuli (lire Acuransurum s ere Cocrargutum,) caleulus rrianculi
Si trianculi cujusvis ulad sive perpendicularis a verrice ab basin) ducalus
t Sermssem Basis, (vet Basis in semissem allicudinis,) emereic area criansal.