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 6
... thefe Elements . In like manner , in the Demonstration of the 26th Prop . of the 11th Book , it is taken for granted ... thefe Propofitions have , for thefe Reasons , been infufficiently demonftrated fince Theon's time hitherto . Befides ...
... thefe Elements . In like manner , in the Demonstration of the 26th Prop . of the 11th Book , it is taken for granted ... thefe Propofitions have , for thefe Reasons , been infufficiently demonftrated fince Theon's time hitherto . Befides ...
Seite 24
... thefe equals the angle ABC ; therefore the angles DBA , ABC are equal to the three angles DBE , EBA , ABC ; but the ... thefe two ftraight lines fhall be in one and the fame ftraight line . At the point B in the straight line AB , let ...
... thefe equals the angle ABC ; therefore the angles DBA , ABC are equal to the three angles DBE , EBA , ABC ; but the ... thefe two ftraight lines fhall be in one and the fame ftraight line . At the point B in the straight line AB , let ...
Seite 25
... thefe alfo are together equal to two right angles ; and CEA , AED have a 15. I E B D been demonstrated to be equal to two right angles ; wherefore the angles CEA , AED are equal to the angles AED , DEB . Take away the common angle AED ...
... thefe alfo are together equal to two right angles ; and CEA , AED have a 15. I E B D been demonstrated to be equal to two right angles ; wherefore the angles CEA , AED are equal to the angles AED , DEB . Take away the common angle AED ...
Seite 26
... . Produce BC to D ; and be- caufe ACD is the exterior angle of the triangle ABC , ACD is greater than the interior and oppofite angle ABC ; to each of B A C D thefe eric fite D b # thefe add the angle ACB 26 THE ELEMENTS.
... . Produce BC to D ; and be- caufe ACD is the exterior angle of the triangle ABC , ACD is greater than the interior and oppofite angle ABC ; to each of B A C D thefe eric fite D b # thefe add the angle ACB 26 THE ELEMENTS.
Seite 27
... thefe add the angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are to- gether equal to two right angles ; therefore the angles ABC b BCA are lefs than two right angles . In like manner ...
... thefe add the angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are to- gether equal to two right angles ; therefore the angles ABC b BCA are lefs than two right angles . In like manner ...
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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.