Philosophiae naturalis principia mathematica . i ; quSe, pef allasmethoJos qusefitse , muko labore temporisque difpendio conftarefolent. Cujus rei exemplo efle poffunt Tradatus Biigenn afiorumque deQuadratura circuli. Nam, ut ex data arcus chorda A, & dimidii ar-cus chorda B, arcum illum proxime affequaris; finge arcum illumeffe z, & circuli radium r% juxtaquefuperioraerit A(nempeduplumfmus dimidii z) = z -±i- ^ =^— 4X5)-- ^X4XI20^^ — &c. EtB=i2;. :Xi6Xi<Xi20it ^&c. Duc jam B in numerum fiftitium «, & a produc- to aufer A, & refidui fecundum terminum (nempe —eo ut evanefcat, pone=o; indeque
Philosophiae naturalis principia mathematica . i ; quSe, pef allasmethoJos qusefitse , muko labore temporisque difpendio conftarefolent. Cujus rei exemplo efle poffunt Tradatus Biigenn afiorumque deQuadratura circuli. Nam, ut ex data arcus chorda A, & dimidii ar-cus chorda B, arcum illum proxime affequaris; finge arcum illumeffe z, & circuli radium r% juxtaquefuperioraerit A(nempeduplumfmus dimidii z) = z -±i- ^ =^— 4X5)-- ^X4XI20^^ — &c. EtB=i2;. :Xi6Xi<Xi20it ^&c. Duc jam B in numerum fiftitium «, & a produc- to aufer A, & refidui fecundum terminum (nempe —eo ut evanefcat, pone=o; indeque emerget 7^=8 2Xl6XSr2 4X610/ , & erit 8B _A = 3^*—, ? &c. hoc elt V = ~; errore tantum exiftente TtTso^»—&c. in exceffu. Quod eft Theorema Hugenlamm. Infuper, fi in Arcus B^, fsgittaAD indefiniteprodufta, qu^raturpunaum G, a quoaftgereaffiGB,Gb abfcindant Tangentem E(?quam proxime aequalem Arcui ifti:Kfto circuli centrum C, diameterAK = ^, &fagittaAD=x: EteritDB (=v<;^9 - 1 I J , Et AE (=AB) ^4;^!-^ —. &e. ^odz EtAE—DB:AD::AE:AG;QuareAG = i^-^^ —,7^—vel-*-& ergo AG = y_ i ^ • a^ viciffim erit DG (W— ? x): DB:: DA: AE —DB. Quare AE —DB = ^-f-^-)-^-4-&c. AddeDB; & 3di Sd prodit AE =</! A:i-(--^H--^-4--^-f-&c. Hoc auferdevaloreip- 7 fius AE fupra habito, & reftabit error —^ -*- vel — &c. Quare inAG, cape AH quintam partem DA, &KG=:HC, &aaaEGBE, F R A G M E N T A. 31 Gbe abfcindent Tangentem E? quam proxime aequalem arcui BA^jerrore tantum exiftente —^ Vdx-^\Q\ — &c. multo minorefcili- cet quam in Theoremate Htigenii. Quodfifiat 7AK:3AH::3DH:»;& capiatur KG = CH — », erit error adhuc multo minor. Atque ita, fi Circuli fegmentum aliquod BA^ per Mechanicam de-ilgnandum eifet: Primo reducerem Aream iltam inlnfinitamfericm, puta hanc ?ibK=%dkx\-~—^ — ^^—Z &c. Dein qus?rerem conftruftiones Mechanicas quibus hanc feriem proxime afTequerer;cujufmodi funt hse : Age reftam AB , &
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