Euclide's Elements ... compendiously demonstrated, by I. Barrow. Transl1660 |
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Σελίδα
... contained in the Three Laft Books , could not be omitted without prejudice & injury ; fince our Author of thefe Elements , being a Sectator of Plato's Schole , is reported to have compiled the whole Syfteme only in reference to that ...
... contained in the Three Laft Books , could not be omitted without prejudice & injury ; fince our Author of thefe Elements , being a Sectator of Plato's Schole , is reported to have compiled the whole Syfteme only in reference to that ...
Σελίδα 20
... contain a greater angle , BDC . Let B D be produced to E. Then is CE + ED a CD . adde BD common to both , then thall be BD + DE + ECCD + BD . Again , BA + AE aBE.6 therefore BA + ACBE + EC.Where- fore 1.BAAC — BD DC . 2. The angle BDC ...
... contain a greater angle , BDC . Let B D be produced to E. Then is CE + ED a CD . adde BD common to both , then thall be BD + DE + ECCD + BD . Again , BA + AE aBE.6 therefore BA + ACBE + EC.Where- fore 1.BAAC — BD DC . 2. The angle BDC ...
Σελίδα 22
... contained under the equall right lines greater then the angle D. For if the angle A be faid to be equall to D , then is the bafe BCEF , which is against the Hypo- thefis If it be faid the angle AD , then 6 will be BCEF , which is alfo ...
... contained under the equall right lines greater then the angle D. For if the angle A be faid to be equall to D , then is the bafe BCEF , which is against the Hypo- thefis If it be faid the angle AD , then 6 will be BCEF , which is alfo ...
Σελίδα 95
... contain EF as one AB - conteins E. which was to be done . PROP . II . If the first AB be equimultiplex te the fecond C , as the third DE is to the fourth F , and if the fifth BG be equi- multiplex to the Jecond Cas the fixth EH is to ...
... contain EF as one AB - conteins E. which was to be done . PROP . II . If the first AB be equimultiplex te the fecond C , as the third DE is to the fourth F , and if the fifth BG be equi- multiplex to the Jecond Cas the fixth EH is to ...
Σελίδα 147
... contain of B ; as 6 = 29 . A ...... 6 6 PROP . V. B ....... G ...... C 12 . D .... 4 4 4 E .... H .... F 8 . If a number A be a part of a number BC , and another number D the fame part of another number EF then both the numbers together ...
... contain of B ; as 6 = 29 . A ...... 6 6 PROP . V. B ....... G ...... C 12 . D .... 4 4 4 E .... H .... F 8 . If a number A be a part of a number BC , and another number D the fame part of another number EF then both the numbers together ...
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...