The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
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Página 40
... gnomon . Thus the paral- A ' lelogram HG , together with the com- ' plements AF , FC , is the gnomon , which is more briefly expressed by ' the letters AGK , or EHC , which are ' at the opposite angles of the paral- ' lelograms which ...
... gnomon . Thus the paral- A ' lelogram HG , together with the com- ' plements AF , FC , is the gnomon , which is more briefly expressed by ' the letters AGK , or EHC , which are ' at the opposite angles of the paral- ' lelograms which ...
Página 43
... gnomon CMG , together with LG , is equal to the rectangle AD , DB , together with the square of CD : but the gnomon CMG and LG makes up the whole figure CEFB , which is the square of CB : there- fore the rectangle AD , DB , together ...
... gnomon CMG , together with LG , is equal to the rectangle AD , DB , together with the square of CD : but the gnomon CMG and LG makes up the whole figure CEFB , which is the square of CB : there- fore the rectangle AD , DB , together ...
Página 44
... gnomon CMG : and DM is the 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 ...
... gnomon CMG : and DM is the 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 ...
Página 45
... gnomon AOH was demonstrated to be quadruple of AK : there- fore four times the rectangle AB , BC is equal to the gnomon AOH . To each of these add XH , which is equal ( Cor . 4. 2. ) to the square of AC : therefore four times the ...
... gnomon AOH was demonstrated to be quadruple of AK : there- fore four times the rectangle AB , BC is equal to the gnomon AOH . To each of these add XH , which is equal ( Cor . 4. 2. ) to the square of AC : therefore four times the ...
Página 146
... gnomon CHL : thereforce CE , or the parallelogram AD is greater , than the parallelogram AF . Next , let AK the base of AF be less than AC , and , the same construction being made , the parallelogram DH is equal to DG ( 36 . 1. ) , for ...
... gnomon CHL : thereforce CE , or the parallelogram AD is greater , than the parallelogram AF . Next , let AK the base of AF be less than AC , and , the same construction being made , the parallelogram DH is equal to DG ( 36 . 1. ) , for ...
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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.