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 sider |
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Side 482
... radius of the circle of which the mea- fure of a given angle is an arch , that arch will contain the fame number of degrees , minutes , feconds , & c . as is mani- feft from Lemma 2 . III . Let AB be produced till it meet the circle ...
... radius of the circle of which the mea- fure of a given angle is an arch , that arch will contain the fame number of degrees , minutes , feconds , & c . as is mani- feft from Lemma 2 . III . Let AB be produced till it meet the circle ...
Side 483
... radius CB to the radius NB , and AE , to MP as AB to BM , and BC or BA to BD as BN or BM to BO ; and , by converfion , DA to MO as AB to MB . Hence the corollary is manifeft ; therefore , if the radius be supposed to be divided into any ...
... radius CB to the radius NB , and AE , to MP as AB to BM , and BC or BA to BD as BN or BM to BO ; and , by converfion , DA to MO as AB to MB . Hence the corollary is manifeft ; therefore , if the radius be supposed to be divided into any ...
Side 484
... radius , the fides become the fines of the angles oppofite to them ; and if either fide be made radius , the remaining fide is the tangent of the angle oppofite to it , and the hypothenufe the fecant of the fame angle . Let ABC be a ...
... radius , the fides become the fines of the angles oppofite to them ; and if either fide be made radius , the remaining fide is the tangent of the angle oppofite to it , and the hypothenufe the fecant of the fame angle . Let ABC be a ...
Side 485
... radius , CE is the fine of the angle CBA , and BD the fine of the angle ACB ; but the two tri angles CAE , DAB have each a right angle at . D and E ; and likewise the common angle CAB ; therefore they are fimilar , and confequently , CA ...
... radius , CE is the fine of the angle CBA , and BD the fine of the angle ACB ; but the two tri angles CAE , DAB have each a right angle at . D and E ; and likewise the common angle CAB ; therefore they are fimilar , and confequently , CA ...
Side 486
... radius is to the tan- gent of an angle ; and the radius is to the tangent of the excess of this angle above half a right angle as the tangent of half the fum of the angles B and C at the base , is to the tangent of half their difference ...
... radius is to the tan- gent of an angle ; and the radius is to the tangent of the excess of this angle above half a right angle as the tangent of half the fum of the angles B and C at the base , is to the tangent of half their difference ...
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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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Side 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...
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.