The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 Seiten |
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Seite 124
... magnitudes , which was here applied to two . ' Q. E. D. IF PROP . II . THEOR ( F the first magnitude be the fame multiple of the fe- cond that the third is of the fourth , and the fifth the fame multiple of the fecond that the fixth is ...
... magnitudes , which was here applied to two . ' Q. E. D. IF PROP . II . THEOR ( F the first magnitude be the fame multiple of the fe- cond that the third is of the fourth , and the fifth the fame multiple of the fecond that the fixth is ...
Seite 127
... magnitude be the fame multiple of another , See N. which a magnitude taken from the first is of a mag- nitude taken from the other ; the remainder fhall be the fame multiple of the remainder , that the whole is of the whole . Let the ...
... magnitude be the fame multiple of another , See N. which a magnitude taken from the first is of a mag- nitude taken from the other ; the remainder fhall be the fame multiple of the remainder , that the whole is of the whole . Let the ...
Seite 128
... magnitude , & c . Q. E. D. See N. 1F PROP . VI . THEOR . F two magnitudes be equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are either equal to thefe others , or equi- multiples ...
... magnitude , & c . Q. E. D. See N. 1F PROP . VI . THEOR . F two magnitudes be equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are either equal to thefe others , or equi- multiples ...
Seite 129
... magnitudes has to the fecond , the see N. fame ratio which the third has to the fourth ; then , if the first be greater ... magnitude A be to B , as C is to D , then alfo inversely B is to A , as D to C. Take of B and D any equimultiples ...
... magnitudes has to the fecond , the see N. fame ratio which the third has to the fourth ; then , if the first be greater ... magnitude A be to B , as C is to D , then alfo inversely B is to A , as D to C. Take of B and D any equimultiples ...
Seite 132
... magnitudes , the greater has a greater ratio to the fame than the lefs has ; and the fame magnitude has a greater ratio to the lefs , than it has to the greater . Fig . 1 . Let AB , BC be unequal magnitudes , of which AB is the greater ...
... magnitudes , the greater has a greater ratio to the fame than the lefs has ; and the fame magnitude has a greater ratio to the lefs , than it has to the greater . Fig . 1 . Let AB , BC be unequal magnitudes , of which AB is the greater ...
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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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 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...
Seite 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.