The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 sider |
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Side 29
... Take a ftraight line DE terminated at the point D , but un- limited towards E , and make a DF equal to A , FG to B , and GH equal to C ; and from the centre F , at the diftance FD , defcribe the circle DKL ; and D from the centre G , at ...
... Take a ftraight line DE terminated at the point D , but un- limited towards E , and make a DF equal to A , FG to B , and GH equal to C ; and from the centre F , at the diftance FD , defcribe the circle DKL ; and D from the centre G , at ...
Side 30
... Take in CD , CE , any points D , E , and join DE ; and make a the triangle AFG the fides D of which fhall be equal to the three straight lines CD , DE , CE , fo B that CD be equal to AF , CE to AG , and DE to FG ; and because DC , CE ...
... Take in CD , CE , any points D , E , and join DE ; and make a the triangle AFG the fides D of which fhall be equal to the three straight lines CD , DE , CE , fo B that CD be equal to AF , CE to AG , and DE to FG ; and because DC , CE ...
Side 36
... take any point D , and jo'n AD ; and at the point A in the ftraight line AD make the ngle B DAE equal to the angle ADC ; and produce the ftraight line EA to F D A F C Because the straight line AD , which meets the two straight lines BC ...
... take any point D , and jo'n AD ; and at the point A in the ftraight line AD make the ngle B DAE equal to the angle ADC ; and produce the ftraight line EA to F D A F C Because the straight line AD , which meets the two straight lines BC ...
Side 40
... take the triangle FDC from the trapezium ABCF , and from the fame trapezium take the triangle EAB ; the remain- ders therefore are equal , that is , the parallelogram ABCD is equal to the parallelogram EBCF . Therefore parallelograms ...
... take the triangle FDC from the trapezium ABCF , and from the fame trapezium take the triangle EAB ; the remain- ders therefore are equal , that is , the parallelogram ABCD is equal to the parallelogram EBCF . Therefore parallelograms ...
Side 70
... Take E the centre of the circle , and join EA , EB : Then , becaufe AF is equal to FB , and FE common to the two tri- angles AFE , BFE , there are two fides in the one equal to two fides in the other , and the base EA is equal to the ...
... Take E the centre of the circle , and join EA , EB : Then , becaufe AF is equal to FB , and FE common to the two tri- angles AFE , BFE , there are two fides in the one equal to two fides in the other , and the base EA is equal to the ...
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe centre circle ABCD circumference cone confequently cylinder defcribed demonftrated drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fide BC fides fimilar firft firſt folid angle fome fore fphere fquare of AC ftraight line AB ftraight line BC given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs likewife oppofite parallel parallelepipeds parallelogram perpendicular plane angles prifms PROP propofition pyramid ratio of BC rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC wherefore
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Side 472 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Side 170 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Side 105 - DEF are likewise equal (13. i.) to two right angles ; therefore the angles AKB, AMB are equal to the angles DEG, DEF, of which AKB is equal to DEG ; wherefore the remaining angle AMB is equal to the remaining angle DEF.
Side 167 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.
Side 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Side 62 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Side 112 - To describe an equilateral and equiangular pentagon about a given circle. • Let ABCDE be the given circle; it is required to describe an equilateral and equiangular pentagon about the circle ABCDE. Let the angles of a pentagon, inscribed in the circle...
Side 200 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.