The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth, of Euclid |
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Σελίδα 45
The sum of the squares of the two parts into which a straight line is divided is a minimum , when it is bisected . Corollary 4. - The square of one of the legs of a right - angled triangle is equal to the rectangle contained by the sum ...
The sum of the squares of the two parts into which a straight line is divided is a minimum , when it is bisected . Corollary 4. - The square of one of the legs of a right - angled triangle is equal to the rectangle contained by the sum ...
Σελίδα 126
If any angle of a triangle be bisected by a straight line which also cuts the base , the segments of the base have the same ratio to one another which the adjacent sides of the triangle have ; and conversely , if the segments of the ...
If any angle of a triangle be bisected by a straight line which also cuts the base , the segments of the base have the same ratio to one another which the adjacent sides of the triangle have ; and conversely , if the segments of the ...
Σελίδα 127
If the exterior angle of a triangle be bisected by a straight line which cuts the base produced , the segments between the bisecting line and the extremities of the base , have to one another the same ratio which the adjacent sides of ...
If the exterior angle of a triangle be bisected by a straight line which cuts the base produced , the segments between the bisecting line and the extremities of the base , have to one another the same ratio which the adjacent sides of ...
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A B C ABCD altitude applied base bisected Book Cassell's centre circle circumference cloth coincide common cone Const contained Corollary cylinder definition demonstration described diagonal diameter divided double draw Edition equal equal angles equiangular equimultiples Exercise extremities fore four fourth given straight line greater half Illustrated inscribed interior join less magnitudes manner meet multiple parallel parallelogram parallelopiped pass perpendicular plane polygon prism PROBLEM produced PROP proportionals proposition proved pyramid ratio reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle sphere square straight lines A B taken THEOREM third touch triangle triangle ABC twice vertex Vols Wherefore whole