The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 sider |
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Resultater 1-5 af 100
Side 18
... THEOR . F two angles of a triangle be equal to one another , the fides alfo which fubtend , or are oppofite to , the equal angles , fhall be equal to one another . Let Let ABC be a triangle having the angle ABC equal 18 THE ELEMENTS.
... THEOR . F two angles of a triangle be equal to one another , the fides alfo which fubtend , or are oppofite to , the equal angles , fhall be equal to one another . Let Let ABC be a triangle having the angle ABC equal 18 THE ELEMENTS.
Side 19
... THEOR . b 4. 5 . PON the fame bafe , and on the fame fide of it , See N. there cannot be two triangles that have their fides which are terminated in one extremity of the base equal to one another , and likewife thofe which are ...
... THEOR . b 4. 5 . PON the fame bafe , and on the fame fide of it , See N. there cannot be two triangles that have their fides which are terminated in one extremity of the base equal to one another , and likewife thofe which are ...
Side 20
... THEOR . I to F two triangles have two fides of the one equal to two fides of the other , each to each , and have like wife their bafes equal ; the angle which is contained by the two fides of the one fhall be equal to the angle con ...
... THEOR . I to F two triangles have two fides of the one equal to two fides of the other , each to each , and have like wife their bafes equal ; the angle which is contained by the two fides of the one fhall be equal to the angle con ...
Side 26
... THEOR . a . 10. I. IF one fide of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its fide BC be produced to D , the exterior angle ACD is greater than ...
... THEOR . a . 10. I. IF one fide of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its fide BC be produced to D , the exterior angle ACD is greater than ...
Side 27
... THEOR . HE greater fide of every triangle is oppofite to the T greater angle . THE Let ABC be a triangle , of which the fide AC is greater than the fide AB ; the angle ABC is also greater than the angle BCA . Because AC is greater than ...
... THEOR . HE greater fide of every triangle is oppofite to the T greater angle . THE Let ABC be a triangle , of which the fide AC is greater than the fide AB ; the angle ABC is also greater than the angle BCA . Because AC is greater than ...
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Almindelige termer og sætninger
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
Populære passager
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.