The Elements of Euclid: The Errors by which Theon, Or Others, Have Long Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthJ. Collingwood, 1827 - 513 Seiten |
Im Buch
Ergebnisse 1-5 von 93
Seite 12
... sides , which are terminated in one extremity of the base , equal to another , and likewise those which are ... BA and AC shall coincide with ED and DF : for , if the base BC coincides with the base EF , but the sides BA , CA do not ...
... sides , which are terminated in one extremity of the base , equal to another , and likewise those which are ... BA and AC shall coincide with ED and DF : for , if the base BC coincides with the base EF , but the sides BA , CA do not ...
Seite 18
... side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB : the angle ABC shall be greater than the angle BCA . * B A Because AC is greater than AB , make * AD ...
... side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB : the angle ABC shall be greater than the angle BCA . * B A Because AC is greater than AB , make * AD ...
Seite 19
... side . Let ABC be a triangle : any two sides of it together shall be greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to the point D ...
... side . Let ABC be a triangle : any two sides of it together shall be greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , CA greater than AB . Produce BA to the point D ...
Seite 20
... sides BA , AC of the triangle , but shall contain an angle BDC greater than the angle BAC . * Produce BD to E ; and because two sides of a triangle are greater than the third side , the two sides BA , AE , of the triangle ABE are ...
... sides BA , AC of the triangle , but shall contain an angle BDC greater than the angle BAC . * Produce BD to E ; and because two sides of a triangle are greater than the third side , the two sides BA , AE , of the triangle ABE are ...
Seite 22
... sides BA , AC are equal to the two ED , DG , each to each , and the angle BAC is D E G F + Constr . equal to the angle EDG ; there- fore the base BC is equal to the base EG . And because DG is equal to DF , the angle DFG is equal to the ...
... sides BA , AC are equal to the two ED , DG , each to each , and the angle BAC is D E G F + Constr . equal to the angle EDG ; there- fore the base BC is equal to the base EG . And because DG is equal to DF , the angle DFG is equal to the ...
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm multiple parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles ROBERT SIMSON segment shewn sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR triangle ABC vertex wherefore
Beliebte Passagen
Seite 141 - 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 40 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Seite 26 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite upon the same side, and also the two interior angles upon the same side together equal to two right angles.
Seite 46 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 28 - Cor. angles; that is * together with four right angles. There1s, 1. fore 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 21 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Seite 12 - IF two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal; the angle. which is contained by the two sides...
Seite 169 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Seite 5 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Seite 97 - 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.