The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 sider |
Fra bogen
Resultater 1-5 af 54
Side 119
... fourth , when any equimultiples whatsoever of the firft and third being taken , and any equimultiples whatfoever of the fecond and fourth ; if the multiple of the first be less than that of the fecond , the multiple of the third is also ...
... fourth , when any equimultiples whatsoever of the firft and third being taken , and any equimultiples whatfoever of the fecond and fourth ; if the multiple of the first be less than that of the fecond , the multiple of the third is also ...
Side 120
... fourth . VI . Magnitudes which have the fame ratio are called proportionals , N. B. When four magnitudes are proportionals , it is • ufually expreffed by saying , the firft is to the second , as the third to the fourth . ' VII . When of ...
... fourth . VI . Magnitudes which have the fame ratio are called proportionals , N. B. When four magnitudes are proportionals , it is • ufually expreffed by saying , the firft is to the second , as the third to the fourth . ' VII . When of ...
Side 121
... fourth ; or that the first is to the third , as the second to the fourth : As is hown in the 16th prop . of this 5th book . XIV . Invertendo , by inversion : When there are four proportionals , and it is inferred , that the second is to ...
... fourth ; or that the first is to the third , as the second to the fourth : As is hown in the 16th prop . of this 5th book . XIV . Invertendo , by inversion : When there are four proportionals , and it is inferred , that the second is to ...
Side 122
... fourth : Prop . E book 5 . XVIII . Ex aequali ( fc . diftantia ) , or ex aequo , from equality of di- ftance ; when there is any number of magnitudes more than two , and as many others , so that they are proportionals when taken two and ...
... fourth : Prop . E book 5 . XVIII . Ex aequali ( fc . diftantia ) , or ex aequo , from equality of di- ftance ; when there is any number of magnitudes more than two , and as many others , so that they are proportionals when taken two and ...
Side 124
... fourth , and the fifth the fame multiple of the fecond that the fixth is of the fourth ; then shall the first together with the fifth be the fame multiple of the fecond , that the third together with the fixth is of the fourth . Let AB ...
... fourth , and the fifth the fame multiple of the fecond that the fixth is of the fourth ; then shall the first together with the fifth be the fame multiple of the fecond , that the third together with the fixth is of the fourth . Let AB ...
Andre udgaver - Se alle
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.