The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
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Página 11
... third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite . A Ꭰ Let ABC , DEF be two triangles which have the two sides AB , AC ...
... third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite . A Ꭰ Let ABC , DEF be two triangles which have the two sides AB , AC ...
Página 21
... third side . * Let ABC be a triangle ; any two sides of it together are 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 ...
... third side . * Let ABC be a triangle ; any two sides of it together are 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 ...
Página 22
... third ( 20. 1 . ) * Let A , B , C be the three given straight lines , of which any two whatever are greater than the third , viz . A and B greater than C ; A and C greater than B ; and B and C than A. It is required to make a triangle ...
... third ( 20. 1 . ) * Let A , B , C be the three given straight lines , of which any two whatever are greater than the third , viz . A and B greater than C ; A and C greater than B ; and B and C than A. It is required to make a triangle ...
Página 25
... third angle BAC to the third angle EDF . For , if AB be not equal B to DE , one of them must be the greater . C E F Let AB be the greater of the two , and make BG equal to DE and join GC ; therefore , because BG is equal to DE , and BC ...
... third angle BAC to the third angle EDF . For , if AB be not equal B to DE , one of them must be the greater . C E F Let AB be the greater of the two , and make BG equal to DE and join GC ; therefore , because BG is equal to DE , and BC ...
Página 26
... third angle BAC to the third angle EDF . Therefore , if two triangles , & c . Q. E. D. PROP . XXVII . THEOR . Ir a straight line falling upon two other straight lines makes the alternate angles equal to one another , these two straight ...
... third angle BAC to the third angle EDF . Therefore , if two triangles , & c . Q. E. D. PROP . XXVII . THEOR . Ir a straight line falling upon two other straight lines makes the alternate angles equal to one another , these two straight ...
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Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone 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 gles gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC square of BC straight line AB straight line BC tangent THEOR triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 34 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Página 143 - 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.
Página 63 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 246 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Página 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 119 - 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.
Página 19 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 12 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.
Página 78 - 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...
Página 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.