The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 Seiten |
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Seite 25
... common angle ABC , the remaining angle ABE is equal to the remaining b 3. Ax . angle ABD , the lefs to the greater , which is impoffible ; there fore BE is not in the fame ftraight line with BC . And , in like manner , it may be ...
... common angle ABC , the remaining angle ABE is equal to the remaining b 3. Ax . angle ABD , the lefs to the greater , which is impoffible ; there fore BE is not in the fame ftraight line with BC . And , in like manner , it may be ...
Seite 35
... common angle BGH , therefore the remaining angle AGH is equal to the re- maining angle GHD ; and they are alternate angles ; there- fore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. I PROP . XXIX . THEOR . this ...
... common angle BGH , therefore the remaining angle AGH is equal to the re- maining angle GHD ; and they are alternate angles ; there- fore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. I PROP . XXIX . THEOR . this ...
Seite 38
... common to the two triangles ABC , DCB , the two fides AB , BC are e- qual to the two DC , CB ; and the angle ABC is equal to the angle BCD ; therefore the bafe AC is equal to the base BD , and the triangle ABC to the triangle BCD , and ...
... common to the two triangles ABC , DCB , the two fides AB , BC are e- qual to the two DC , CB ; and the angle ABC is equal to the angle BCD ; therefore the bafe AC is equal to the base BD , and the triangle ABC to the triangle BCD , and ...
Seite 39
... common to the two triangles , which is adjacent to their equal angles ; there- fore their other fides fhall be equal , each to each , and the third angle of the one to the third angle of the other b , viz . b 26. s . the fide AB to the ...
... common to the two triangles , which is adjacent to their equal angles ; there- fore their other fides fhall be equal , each to each , and the third angle of the one to the third angle of the other b , viz . b 26. s . the fide AB to the ...
Seite 40
... common ; therefore the whole , or the remain- der , AE is equal to the whole , or the remainder DF ; AB al- fo is equal to DC ; and the two EA , AB are therefore equal to A DE FAE DF WW B C B C the two FD , DC , each to each ; and the ...
... common ; therefore the whole , or the remain- der , AE is equal to the whole , or the remainder DF ; AB al- fo is equal to DC ; and the two EA , AB are therefore equal to A DE FAE DF WW B C B C the two FD , DC , each to each ; and the ...
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Häufige Begriffe und Wortgruppen
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.