Euclide's Elements ... compendiously demonstrated, by I. Barrow. Transl


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Σελίδα 25 - 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 74 - 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 99 - Proportions that are one and the fame to any "Third, are alfo the fame to one another.
Σελίδα 289 - 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 96 - 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 268 - 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 140 - XA number oddly odd, is that which an odd number meafureth by an odd number.
Σελίδα 33 - 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 33 - AB, AC, containing the right angle. "join AE, and AD ; and draw AM parallel to CE...

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