The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 Seiten |
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Seite 38
... parallel ftraight lines , towards the fame parts , are also themselves equal and parallel . Let AB , CD be equal and pa- A rallel ftraight lines , and joined towards the fame parts by the ftraight lines AC , BD ; AC , BD are alfo equal ...
... parallel ftraight lines , towards the fame parts , are also themselves equal and parallel . Let AB , CD be equal and pa- A rallel ftraight lines , and joined towards the fame parts by the ftraight lines AC , BD ; AC , BD are alfo equal ...
Seite 39
... parallel to BD ; and it was shown to be equal to it . Therefore ftraight lines , & c . Q. E. D. TH PROP . XXXIV . THEOR . HE oppofite fides and angles of parallelograms are equal to one another , and the diameter bifects them , that is ...
... parallel to BD ; and it was shown to be equal to it . Therefore ftraight lines , & c . Q. E. D. TH PROP . XXXIV . THEOR . HE oppofite fides and angles of parallelograms are equal to one another , and the diameter bifects them , that is ...
Seite 41
... parallel ftraight lines towards the fame parts , are themselves equal and parallel ; therefore EB , CH are both equal and parallel , and b 33. I. EBCH is a parallelogram ; and it is equal to ABCD , because c 35. 1 . it is upon the fame ...
... parallel ftraight lines towards the fame parts , are themselves equal and parallel ; therefore EB , CH are both equal and parallel , and b 33. I. EBCH is a parallelogram ; and it is equal to ABCD , because c 35. 1 . it is upon the fame ...
Seite 42
... parallel a to CA , and through F draw FH parallel to ED : Then each of G the figures GBCA , DEFH is a paralle logram ; and they are equal to one an- other , because they are upon equal bafes BC , EF , and between the fame parallels B C ...
... parallel a to CA , and through F draw FH parallel to ED : Then each of G the figures GBCA , DEFH is a paralle logram ; and they are equal to one an- other , because they are upon equal bafes BC , EF , and between the fame parallels B C ...
Seite 43
... parallel to BC . In the fame manner , it can be demonstrated that no other line but AD is parallel to B BC ; AD is therefore parallel to it . Wherefore equal triangles upon , & c . Q. E D. 6 PROP . XL . THEOR . Etraight line , and ...
... parallel to BC . In the fame manner , it can be demonstrated that no other line but AD is parallel to B BC ; AD is therefore parallel to it . Wherefore equal triangles upon , & c . Q. E D. 6 PROP . XL . THEOR . Etraight line , and ...
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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.