The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 Seiten |
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Seite 102
... DEFINITION S. I. Rectilineal figure is faid to be infcribed in another recti- lineal figure , when all the angles of the infcribed figure are upon the fides of the figure in which it is infcribed , each upon each . II . In like manner ...
... DEFINITION S. I. Rectilineal figure is faid to be infcribed in another recti- lineal figure , when all the angles of the infcribed figure are upon the fides of the figure in which it is infcribed , each upon each . II . In like manner ...
Seite 119
... DEFINITIONS . J. Lefs magnitude is faid to be a part of a greater magni- tude , when the lefs measures the greater , that is , when the lefs is contained a certain number of times exactly in the greater . ' II . A greater magnitude is ...
... DEFINITIONS . J. Lefs magnitude is faid to be a part of a greater magni- tude , when the lefs measures the greater , that is , when the lefs is contained a certain number of times exactly in the greater . ' II . A greater magnitude is ...
Seite 120
... definition ) the multiple of the firft is greater than that of the fecond , but the multiple of the third is not greater than the multiple of the fourth ; then the first is faid to have to the fecond a greater ratio than the third magni ...
... definition ) the multiple of the firft is greater than that of the fecond , but the multiple of the third is not greater than the multiple of the fourth ; then the first is faid to have to the fecond a greater ratio than the third magni ...
Seite 121
... definition , A is faid to have to D. the ratio compounded of ratios which are the fame with the ratios of E to F , G to H , and K to L : And the fame thing is to be understood when it is more briefly expreffed , by faying A has to D the ...
... definition , A is faid to have to D. the ratio compounded of ratios which are the fame with the ratios of E to F , G to H , and K to L : And the fame thing is to be understood when it is more briefly expreffed , by faying A has to D the ...
Seite 122
... definition ; whence this is called ordinate proportion . It is demonftrated in 22d prop . book 5 . XX . Ex aequali , in proportione perturbata , feu inordinata ; from e- quality , in perturbate or diforderly proportion * ; this term is ...
... definition ; whence this is called ordinate proportion . It is demonftrated in 22d prop . book 5 . XX . Ex aequali , in proportione perturbata , feu inordinata ; from e- quality , in perturbate or diforderly proportion * ; this term is ...
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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.