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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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LCV O I
ralleta elt ipsi S N, _ n C ipti v MI, aequalia sunt etiam Friangula A BD, A Cin
aequales Tune igitur ANY e Au; AM et Ad; AD e An; AC a AB. Guate
dempeis concinuo aequalibus, aequales crunt L E e nd; D e dn; DC e 1B
Problema.
Data media trium proportionalium, ec differentia extremarum, dare extremas.
Sit media data AD, eique ad rectos angulos ponatur DZ. aequalis differentix Fis. 17.
excremarum, e diridatur bitariam in S, centro aurem S ee interrallo SD deleri-
hacur circulus D e n _ per S ducta A e Sn; DOnatuT A M aequalis A H, e AC X
qualis An. Duoniam AD cansic circulum, ergo quadratum AD aequale est rectan-
sulOP. AM; ergo AM, AD, A C, Tunc in concinua proportione, et M C. (ditterentia
Extremarum) aequalis cA iPAD L
Lemma.
Si Fuerine maenicudines in intinitum decrescences summa Dil.
Ferentiarum aequatur maximo Termino.
Sinc magnicudines a Z, b, C, d, egc. in intinitum: dico omnes
earum ditterentias aequari ip(I a Z SIReGCEUE; Une majores e
Fane aB, 27, 28, 85. xequales iplis b, C, d, eC; crunt ergo
2, 78, 8c. Parres iplius a L; non sune ergo majores P0-
t0. Sint jam minores, quare aequales sint ipsi Z S, reliquo autem
ad aqualis Ponatur d ipla etiam d pOnaTUT aE minOr; erso ad
dira elt alia ditterencia d’e, quare Z. est aequalis summa omnium
differentiarum, ergo Z. dxqualis elt ip( ZC, major minori, quod
cl abTurdum. F. r5O L a (eum lit neque major neque minor) aequa-
lis elt Cummae omnium in intinicum ditferentiarum.
Temma.
Binarum magnicudinum ditterentia, aequalis est disserentixe incer summam de du-
plum urriulris. Patet addendo ucrique masnicudini minimam, vel ucrique maximam.
Desinitio.
Polreonum Serracum est figura constans alcernatim ex lateribus sibi invicem pa-
rallelis, e laceribus obliquis. Sola aurem lacera non parallela rocentur simplici
ter Latera.
Polysonum Serracum circulo Circundari dicitur, quando unusquisque angulus FiB. V7
internus circulum artingit. Acque idem circulo inseri dicitur, quando unusquisque
angulus externus circulum accinsis, et angulum incernum polysoni circundari ad
verricem habet.
Problema.
Poirsonum Serratum lemicireulo daco inserere, cujus summa lacerum sic duolo
diametri minor; acque aliud circundaro cujus summa lacerum sic duplo diametri
major; ita tamen uc uriulque lummae disterentia sic datae cuieinque magnicudini
aequalis.
Sic Cemicireulus datus A DD, cujuscliameter Cic A D; maxnicudo dara X. Data
isitur media proporrionalium AD, tianc AM, AD, A C. concinue proportionales,
ita ut difterencia extremarum M C, aequalis sIC iPSi X. Disponantur autem subrenix
AD ubique in data ratione A D ad A M, e continuetur ratio in intinitum. Pro.
ductis deinde subtensis, per unumquodque D ducantur parallelae N DB, ad prOXI
mam urrinque subtentam. Patet ex iis quae dicta sune, Polysonum semicirculo in
Terrum este. Rcque aliud circundarum. Dieo autem insuper latera Inlerri simul
Tumpta (seilicet omnes in intinitum D N) deticere a duxlo diamerri delectu D, M:
Lacera vero circundari (scilicet omnes in intinitum BD) excedere duplum dia-
metri, excellu DC: difterenciam denique lacerum urriusque aequalem esse daix
Diametris AN e AC, ala CC Caspenes eriam in A, d Lecances IlV.
tenlas
Fig. 19
cub
magnicudini Z.