The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected; and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. the first six books, together with the eleventh and twelfthJ. Nourse, London, and J. Balfour, Edinburgh, 1775 - 520 Seiten |
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Seite 26
... bifected , it may be demonstrated that the angle BCG , that is , the angle ACD , is greater than the angle ABC . Therefore , if one fide , & c . Q. E. D. A PROP . XVII . THEOR . NY two angles of a triangle are together less than two ...
... bifected , it may be demonstrated that the angle BCG , that is , the angle ACD , is greater than the angle ABC . Therefore , if one fide , & c . Q. E. D. A PROP . XVII . THEOR . NY two angles of a triangle are together less than two ...
Seite 56
... bifected , and produced to any point ; the rectangle contained by the whole line thus produced , and the part of it produced , together with the fquare of half of the line bifected , is equal to the fquare of the ftraight line which is ...
... bifected , and produced to any point ; the rectangle contained by the whole line thus produced , and the part of it produced , together with the fquare of half of the line bifected , is equal to the fquare of the ftraight line which is ...
Seite 60
... bifected , and of the fquare of the line made up of the half and the part pro- duced . Let the ftraight line AB be bifected in C , and produced to the point D ; the fquares of AD , DB are double of the fquares of AC , CD . From the ...
... bifected , and of the fquare of the line made up of the half and the part pro- duced . Let the ftraight line AB be bifected in C , and produced to the point D ; the fquares of AD , DB are double of the fquares of AC , CD . From the ...
Seite 62
... bifected in E , and produced to the point F , the rectangle CF , FA , to- gether with the fquare of AE , is equal d to the fquare of EF : But EF is equal to EB ; therefore the rectangle CF , FA , toge- ther with the fquare of AE , is ...
... bifected in E , and produced to the point F , the rectangle CF , FA , to- gether with the fquare of AE , is equal d to the fquare of EF : But EF is equal to EB ; therefore the rectangle CF , FA , toge- ther with the fquare of AE , is ...
Seite 70
... bifect it . Let ABC be a circle ; and let CD , a ftraight line drawn through the center bifect any straight line AB , which does not pafs through the center , in the point F : It cuts it also at right angles . Take 2 E the center of the ...
... bifect it . Let ABC be a circle ; and let CD , a ftraight line drawn through the center bifect any straight line AB , which does not pafs through the center , in the point F : It cuts it also at right angles . Take 2 E the center of the ...
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle bifected Book XI cafe circle ABCD circumference cone confequently cylinder defcribed demonftrated diameter drawn equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fhall fhewn fide BC fimilar firft firſt folid angle fome fore fphere fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs likewife line BC oppofite parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles thefe THEOR theſe triangle ABC vertex wherefore
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Seite 32 - 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 165 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF.
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 10 - When several angles are at one point B, any ' one of them is expressed by three letters, of which ' the letter that is at the vertex of the angle, that is, at ' the point in which the straight lines that contain the ' angle meet one another, is put between the other two ' letters, and one of these two is...
Seite 55 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Seite 32 - ... then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.
Seite 45 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Seite 211 - AB shall be at right angles to the plane CK. Let any plane DE pass through AB, and let CE be the common section of the planes DE, CK ; take any point F in CE, from which draw FG in the plane DE at right D angles to CE ; and because AB is , perpendicular to the plane CK, therefore it is also perpendicular to every straight line in that plane meeting it (3.
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.
Seite 304 - Thus, if B be the extremity of the line AB, or the common extremity of the two lines AB, KB, this extremity is called a point, and has no length : For if it have any, this length must either be part of the length of the line AB, or of the line KB.