The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 49
... gnomon , F K BG C which is more briefly expressed by the let- ' ters AGK , or EHC , which are at the opposite · angles of the parallelograms which make the gnomon . ' F * 11 . 1 . * 3. 1 . * 49 ...
... gnomon , F K BG C which is more briefly expressed by the let- ' ters AGK , or EHC , which are at the opposite · angles of the parallelograms which make the gnomon . ' F * 11 . 1 . * 3. 1 . * 49 ...
Page 54
... gnomon 2. and 34. 1 . +2 Ax . * C DB L H M K E G F +1 Ax . CMG ; therefore the gnomon CMG is equal † to the rectangle AD , DB : to each of these add LG , * Cor . 4. which is equal to the square of CD ; therefore the gnomon CMG ...
... gnomon 2. and 34. 1 . +2 Ax . * C DB L H M K E G F +1 Ax . CMG ; therefore the gnomon CMG is equal † to the rectangle AD , DB : to each of these add LG , * Cor . 4. which is equal to the square of CD ; therefore the gnomon CMG ...
Page 55
... gnomon CMG ; but AM +2 Ax . is the rectangle contained by AD , DB , for DM is equal to DB : therefore the gnomon CMG is * Cor . 4 . equal to the rectangle AD , DB : add to each of these LG , which is equal to the square of CB , +1 Ax ...
... gnomon CMG ; but AM +2 Ax . is the rectangle contained by AD , DB , for DM is equal to DB : therefore the gnomon CMG is * Cor . 4 . equal to the rectangle AD , DB : add to each of these LG , which is equal to the square of CB , +1 Ax ...
Page 56
... gnomon AKF , together with the square +1 Ax . CK , is equal to twice the rectangle AB , BC : + Cor . 4. to each of these equals add HF , which is equal † to the square of AC : therefore the gnomon AKF , together with the squares CK , HF ...
... gnomon AKF , together with the square +1 Ax . CK , is equal to twice the rectangle AB , BC : + Cor . 4. to each of these equals add HF , which is equal † to the square of AC : therefore the gnomon AKF , together with the squares CK , HF ...
Page 57
... gnomon AOH was demonstrated to be quadruple of AK ; therefore four times the rectangle AB , BC is equal to the gnomon AOH to each of +1 Ax . these add XH , which is equal to the square of * Cor . 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 gnomon AOH to each of +1 Ax . these add XH , which is equal to the square of * Cor . AC ; therefore four times the rectangle ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole