The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
Dentro del libro
Página 12
... angles of the one shall coincide with the remaining angles of the other and be equal to them , viz , the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two triangles have two sides of the one equal to two sides ...
... angles of the one shall coincide with the remaining angles of the other and be equal to them , viz , the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two triangles have two sides of the one equal to two sides ...
Página 13
... angle GCB , and the angle BCF to the angle CBG ; and , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; the remaining angle ABC is ...
... angle GCB , and the angle BCF to the angle CBG ; and , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; the remaining angle ABC is ...
Página 18
... angles ; but the angles ABC , ABD are likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common angle ABC , the remaining angle ABE is equal ( 3. Ax . ) to the ...
... angles ; but the angles ABC , ABD are likewise together equal to two right angles ; therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common angle ABC , the remaining angle ABE is equal ( 3. Ax . ) to the ...
Página 19
... angle AED , and the remaining angle CEA is equal ( 3. Ax . ) to the remaining angle DEB . In the same manner it can be de- monstrated that the angles CEB , AED are equal . Therefore , if two straight lines , & c . Q. E. D. D Cor . 1 ...
... angle AED , and the remaining angle CEA is equal ( 3. Ax . ) to the remaining angle DEB . In the same manner it can be de- monstrated that the angles CEB , AED are equal . Therefore , if two straight lines , & c . Q. E. D. D Cor . 1 ...
Página 27
... angles ; and that AGH , BGH are also equal ( 13. 1. ) to two right angles ; the angles AGH , BGH are equal to the angles BGH , GHD : take away the common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ...
... angles ; and that AGH , BGH are also equal ( 13. 1. ) to two right angles ; the angles AGH , BGH are equal to the angles BGH , GHD : take away the common angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ...
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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 straight line AB straight line BC tangent THEOR third three plane angles triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 36 - 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 145 - 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 65 - 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 248 - 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 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 121 - 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 21 - 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 14 - 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 80 - 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 133 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.