The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 sider |
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Resultater 1-5 af 100
Side 16
... fhall be equal to AD ; but the ftraight line C is likewife equal to AD ; whence AE and C are each of them equal to ... fhall likewife have their bafes , or third fides , equal ; and the two triangles fhall be equal ; and their other ...
... fhall be equal to AD ; but the ftraight line C is likewife equal to AD ; whence AE and C are each of them equal to ... fhall likewife have their bafes , or third fides , equal ; and the two triangles fhall be equal ; and their other ...
Side 17
... fhall be equal each to each , viz . the angle ABCB to the angle DEF , and the angle ACB to DFE .. CE Book I. D F For ... fhall coincide with the point E , becaufe AB is equal to DE ; and AB coinciding with DE , AC fhall coincide with DF ...
... fhall be equal each to each , viz . the angle ABCB to the angle DEF , and the angle ACB to DFE .. CE Book I. D F For ... fhall coincide with the point E , becaufe AB is equal to DE ; and AB coinciding with DE , AC fhall coincide with DF ...
Side 18
... fhall be equal to the angle ACB , and the angle CBD to the angle BCE . a 3. 1 . b 4. I. C 3. Ax . In BD take any point F , and from AE , the greater , cut off AG equal to AF , the lefs , and join FC , GB . A Because AF is equal to AG ...
... fhall be equal to the angle ACB , and the angle CBD to the angle BCE . a 3. 1 . b 4. I. C 3. Ax . In BD take any point F , and from AE , the greater , cut off AG equal to AF , the lefs , and join FC , GB . A Because AF is equal to AG ...
Side 20
... fhall be equal to the angle con tained by the two fides equal to them , of the other . Let ABC , DEF be two triangles having the two fides AB , AC equal to the two fides DE , DF , each to each , viz . AB to DE , and AC to A DF ; and ...
... fhall be equal to the angle con tained by the two fides equal to them , of the other . Let ABC , DEF be two triangles having the two fides AB , AC equal to the two fides DE , DF , each to each , viz . AB to DE , and AC to A DF ; and ...
Side 21
... fhall coincide with ED and DF ; for , if the bafe BC cain- cides with the base EF , but the fides BA , CA do not coin- cide with the fides ED , FD , but have a different fituation , as EG , FG ; then , upon the fame bafe EF , and upon ...
... fhall coincide with ED and DF ; for , if the bafe BC cain- cides with the base EF , but the fides BA , CA do not coin- cide with the fides ED , FD , but have a different fituation , as EG , FG ; then , upon the fame bafe EF , and upon ...
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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.