Euclide's Elements ... compendiously demonstrated, by I. Barrow. Transl1660 |
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Σελίδα 23
... say BC EG , and AC DG , and the angle A For if EG be greater then BC , make EI joyn the line DI . Now because ABg BC b - will be the angle EID EI , and the angle GgE ; abfurd . Therefore is B C byp . EDG . BC , and ED , and therefore ...
... say BC EG , and AC DG , and the angle A For if EG be greater then BC , make EI joyn the line DI . Now because ABg BC b - will be the angle EID EI , and the angle GgE ; abfurd . Therefore is B C byp . EDG . BC , and ED , and therefore ...
Σελίδα 75
... say that that line DB fo falling fhall touch the circle given . From the point Dalet a tangent DF be drawn , a 17.3 . and from the centre E draw ED , LB , EF . - Now be- caufe DBqb ADC DFq , therefore is DB b byp . DE : But EB EF , and ...
... say that that line DB fo falling fhall touch the circle given . From the point Dalet a tangent DF be drawn , a 17.3 . and from the centre E draw ED , LB , EF . - Now be- caufe DBqb ADC DFq , therefore is DB b byp . DE : But EB EF , and ...
Σελίδα 89
... say it's done . For the angle CGD.— of 2 right AGFA GB . ' c Therefore B G C = FGE ; therefore the d arches and e fub- DGE 32. 1 $ 15.4 d26.3 . Cor.13.1 . 29.1 of 2 right : tenfes AB , BC , CD , DE , EF are equall . Therefore the ...
... say it's done . For the angle CGD.— of 2 right AGFA GB . ' c Therefore B G C = FGE ; therefore the d arches and e fub- DGE 32. 1 $ 15.4 d26.3 . Cor.13.1 . 29.1 of 2 right : tenfes AB , BC , CD , DE , EF are equall . Therefore the ...
Σελίδα 101
... say that A. B :: C. D. Take G , H , I , the equimultiplices of A , C , E ; and K , L , M the equimultiplices of B , D , F. Now a because A.B :: E.FifG , K , b then a byp . after the fame manner IC , M. And likewise because E. F :: C. D. ...
... say that A. B :: C. D. Take G , H , I , the equimultiplices of A , C , E ; and K , L , M the equimultiplices of B , D , F. Now a because A.B :: E.FifG , K , b then a byp . after the fame manner IC , M. And likewise because E. F :: C. D. ...
Σελίδα 105
... say that AB . AC :: DE . DF.For by permutation AB.DE :: CB.FE , b there- a 16.5 . fore AB . DE :: AC.DF. whence again by permuta- b . 19.5 . tion AB . AC :: DE . DF . w . w . to be Dem . PROP . a byp bor 4. 5 . Chyp & 8 .. EUCLIDE'S ...
... say that AB . AC :: DE . DF.For by permutation AB.DE :: CB.FE , b there- a 16.5 . fore AB . DE :: AC.DF. whence again by permuta- b . 19.5 . tion AB . AC :: DE . DF . w . w . to be Dem . PROP . a byp bor 4. 5 . Chyp & 8 .. EUCLIDE'S ...
Άλλες εκδόσεις - Προβολή όλων
Euclide's Elements ... Compendiously Demonstrated, by I. Barrow. Transl Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Euclide's Elements ... Compendiously Demonstrated, by I. Barrow. Transl Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Euclide's Elements ... Compendiously Demonstrated, by I. Barrow. Transl Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD Abfurd alfo alſo bafe baſe becauſe bifect binomiall centre circle commenfurable common meaſure confequently confir Coroll cube number defcribed demonftrated diameter dodecaedron draw drawn EFGH equiangular equilaterall faid fame proportion fecond fegment fhall fide fince firft foever folid fome fore fphere fquare number fuperficies fuppofed greater Hence Icofaedron incommenfurable infcribed irrationall leaft leffe leffer likewife line AC magnitudes mediall odde number oppofite parallel parallelepipedons parallelogram pentagone perpendicular prifmes prime number PROP proportionall pyramide quall rationall line rectangle refiduall line refidue right angles right line AB right line given right-lined figure Schol ſhall Space AC ſquare thefe thence thofe thoſe triangle triangle ABC w.w.to be Dem whence wherefore whole line
Δημοφιλή αποσπάσματα
Σελίδα 2 - XV. A Circle is a plain figure contained under one line, which is called a circumference ; unto which all lines, drawn from one point within the figure, and falling upon the circumference thereof, are equal the one to the other. XVI. And that point is called the center of the circle. XVII. A Diameter of a circle is a right-line drawn thro' the center thereof, and ending at the circumference on either fide, dividing the circle into two equal parts.
Σελίδα 27 - ABC, with its adjacent exterior ABD, is equal b to two right angles ; therefore all the interior, together with all the exterior angles of the figure, are equal to twice as many right angles as there are fides of the figure ; that is, by the foregoing corollary, they are equal to all the interior angles of the figure, together with four right angles ; therefore all the exterior angles are equal to four right angles, PROP. XXXIII.
Σελίδα 76 - Right-lined figure is faid to be infcribed iri a. right-lined figure, when every one of the angles of the infcribed figure touch every one of the fides of the figure wherein it is infcribed.
Σελίδα 101 - Proportions that are one and the fame to any "Third, are alfo the fame to one another.
Σελίδα 291 - Right-lined plane Angles equal , from whofe Points equal Right Lines be elevated on the Planes of the Angles, containing equal Angles with the Lines firft given, each to each ; Perpendiculars drawn from the extreme Points of thofe elevated Lines to the Planes of the Angles firft given, are equal to one another.
Σελίδα 98 - AE is the fame ai . c." hiultiple of the whole CF + FD, as the one AE is of the one CF, that is, as AB is of CD ; therefore GE (£)~ b £4 AB; and (<r) fo AE, which is common, being takeri c ^ away, there remains GA=EB, Therefore, &c.
Σελίδα 270 - j from whence it begun to be moved. XXII. The Axis of a Cylinder is that fixed Right Line about which the Parallelogram is turned. XXIII. And the Bafes of a Cylinder are the Circlet that he defcribed by the Motion of the two oppofite Sides of the Parallelogram.
Σελίδα 142 - XA number oddly odd, is that which an odd number meafureth by an odd number.
Σελίδα 35 - Pjthagoiat his theoreme, becaufe he was the inventor of it. By the help of •which the addition and fubftraftion of fquares are performed; to which purpofe lerve the two tdllowjng probleuies.
Σελίδα 35 - AB, AC, containing the right angle. "join AE, and AD ; and draw AM parallel to CE...