The Elements of EuclidDesilver, Thomas, 1838 - 416 sider |
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Resultat 1-5 av 65
Side 41
... rectangle EH is contained by A , EC : therefore the rectangle contained by A , BC is equal to the several rectangles contained by A , BD , and by A , DE ; and also by A , EC . Wherefore , if there be two straight lines , & c . Q. E. D. ...
... rectangle EH is contained by A , EC : therefore the rectangle contained by A , BC is equal to the several rectangles contained by A , BD , and by A , DE ; and also by A , EC . Wherefore , if there be two straight lines , & c . Q. E. D. ...
Side 42
... rectangle contained by the parts . Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares of AC , CB , and to twice the rectangle contained by AC , CB . H A D C B G K F E Upon AB describe ...
... rectangle contained by the parts . Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares of AC , CB , and to twice the rectangle contained by AC , CB . H A D C B G K F E Upon AB describe ...
Side 43
... rectangle con- tained by AD , DB , for DH is equal ( Cor . 4. 2. ) to DB , and DF together with CH is the gnomon CMG ; therefore the gno . mon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal ( 43. 1 ...
... rectangle con- tained by AD , DB , for DH is equal ( Cor . 4. 2. ) to DB , and DF together with CH is the gnomon CMG ; therefore the gno . mon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal ( 43. 1 ...
Side 44
... rectangle contained by AD , DB , for DM is equal ( Cor . 4. 2. ) to DB : therefore the gnomon CMG is equal to the rectangle AD , DB , add to each of these LG , which is equal to the square of CB , therefore the rectangle AD , DB ...
... rectangle contained by AD , DB , for DM is equal ( Cor . 4. 2. ) to DB : therefore the gnomon CMG is equal to the rectangle AD , DB , add to each of these LG , which is equal to the square of CB , therefore the rectangle AD , DB ...
Side 45
... rectangle contained by the whole line , and one of the parts , to- gether 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 . Let the straight line AB be divided ...
... rectangle contained by the whole line , and one of the parts , to- gether 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 . Let the straight line AB be divided ...
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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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 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.
Side 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.
Side 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.
Side 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...
Side 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.