The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 51
... gnomon . Thus the pa- rallelogram HG , together ' with the complements AF , ' FC , is the gnomon , which ' is more briefly expressed ' by the letters AGK , or EHC , which are at the opposite angles of the pa- ' rallelograms which make ...
... gnomon . Thus the pa- rallelogram HG , together ' with the complements AF , ' FC , is the gnomon , which ' is more briefly expressed ' by the letters AGK , or EHC , which are at the opposite angles of the pa- ' rallelograms which make ...
Página 55
... gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal to the square of CD ; therefore the gnomon CMG , together with LG , is equal to the rectangle AD , DB , together with the ...
... gnomon CMG ; therefore the gnomon CMG is equal to the rectangle AD , DB : to each of these add LG , which is equal to the square of CD ; therefore the gnomon CMG , together with LG , is equal to the rectangle AD , DB , together with the ...
Página 56
... gnomon CMG and the figure LG : but the gnomon CMG and LG make up the whole figure CEFD , which is the square of CD ; therefore the rectangle AD , DB , together with the square of CB , is equal to the square of CD . Wherefore , if a ...
... gnomon CMG and the figure LG : but the gnomon CMG and LG make up the whole figure CEFD , which is the square of CD ; therefore the rectangle AD , DB , together with the square of CB , is equal to the square of CD . Wherefore , if a ...
Página 57
... gnomon -AKF together with the square CK ; therefore the gnomon AKF , toge- ther with the square CK , is double of AK : but twice the rectangle AB , BC is double of AK , for BK is equal to BC : therefore the gnomon AKF , together with ...
... gnomon -AKF together with the square CK ; therefore the gnomon AKF , toge- ther with the square CK , is double of AK : but twice the rectangle AB , BC is double of AK , for BK is equal to BC : therefore the gnomon AKF , together with ...
Página 58
... gnomon AOH was demonstrated to be quadruple of AK ; therefore four times the rectangle AB , BC is equal to the d Cor . 4. 2. gnomon AOH . To each of these add XH , which is equal to the square of AC : therefore four times the rectangle ...
... gnomon AOH was demonstrated to be quadruple of AK ; therefore four times the rectangle AB , BC is equal to the d Cor . 4. 2. gnomon AOH . To each of these add XH , which is equal to the square of AC : therefore four times the rectangle ...
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Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid 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 meet 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 solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore