The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 páginas |
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Página 6
... Figures is contained by no more than three plane Angles ; for , in other Cafes , two folid Figures may be contained by fimilar Planes of the fame Number and Mag- nitude , and yet be unequal to one another ; as shall be made evident in ...
... Figures is contained by no more than three plane Angles ; for , in other Cafes , two folid Figures may be contained by fimilar Planes of the fame Number and Mag- nitude , and yet be unequal to one another ; as shall be made evident in ...
Página 7
... Figures in a Circle is added at the End of the fixth Book . Alfo the Note on the 29th Prop . Book ift , is altered , and made more explicit , and a more general Demon- ftration is given , instead of that which was in the Note on the ...
... Figures in a Circle is added at the End of the fixth Book . Alfo the Note on the 29th Prop . Book ift , is altered , and made more explicit , and a more general Demon- ftration is given , instead of that which was in the Note on the ...
Página 10
... figure is that which is inclofed by one or more boundaries . XV . A circle is a plane figure contained by XV . IO THE ELEMENTS Book I. ...
... figure is that which is inclofed by one or more boundaries . XV . A circle is a plane figure contained by XV . IO THE ELEMENTS Book I. ...
Página 11
... figure contained by a diameter and the part of the circumference cut off by the diameter . XIX . A fegment of a circle is the figure contained by a straight " line , and the circumference it cuts off . " XX . Rectilineal figures are ...
... figure contained by a diameter and the part of the circumference cut off by the diameter . XIX . A fegment of a circle is the figure contained by a straight " line , and the circumference it cuts off . " XX . Rectilineal figures are ...
Página 12
... figures , a fquare is that which has all its fide equal , and all its angles right angles . XXXI . An oblong , is ... figures befides thefe , XXXXIV 32 THE ELEMENTS An acute angled triangle, is that which has three ...
... figures , a fquare is that which has all its fide equal , and all its angles right angles . XXXI . An oblong , is ... figures befides thefe , XXXXIV 32 THE ELEMENTS An acute angled triangle, is that which has three ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 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...
Página 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.