The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry from the Edition of Dr. Robert Simson ... With Exercises. By S. A. Good ... Second Edition |
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Σελίδα 49
AF is the rectangle contained by BA , AC , for it is contained by DA , AC , of which AD is equal ( Def . ... square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by the parts .
AF is the rectangle contained by BA , AC , for it is contained by DA , AC , of which AD is equal ( Def . ... square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by the parts .
Σελίδα 50
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 , together with twice the rectangle contained by AC , CB . o B . . : مروان خبر G H K tries Ther , AC , CB D F E Upon AB ...
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 , together with twice the rectangle contained by AC , CB . o B . . : مروان خبر G H K tries Ther , AC , CB D F E Upon AB ...
Σελίδα 51
AG , GE , are equal to twice the rectangle AC , CB : and HF , CK , are the squares of AC , CB ; wherefore 15 . The four figures HF , CK , AG , GE , are equal to the squares of AC , CB , and to twice the rectangle AC , CB : but HF ...
AG , GE , are equal to twice the rectangle AC , CB : and HF , CK , are the squares of AC , CB ; wherefore 15 . The four figures HF , CK , AG , GE , are equal to the squares of AC , CB , and to twice the rectangle AC , CB : but HF ...
Σελίδα 53
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 .
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 .
Σελίδα 54
The squares of AB and BC are equal to twice the rectangle AB , BC , together with the square of AC . Wherefore , if a straight line , & c . Q.E.D. a PROP . VIII . - THEOREM . If a straight line be divided into any two parts , four times ...
The squares of AB and BC are equal to twice the rectangle AB , BC , together with the square of AC . Wherefore , if a straight line , & c . Q.E.D. a PROP . VIII . - THEOREM . If a straight line be divided into any two parts , four times ...
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AB is equal ABC is equal ABCD angle ABC angle ACB angle AGH angle BAC angle BCD angle equal base BC bisected centre circle ABC circumference coincide common demonstrated describe diameter distance divided double draw equal angles exterior angle extremity fall figure four given circle given point given straight line gnomon greater impossible inscribed join less Let ABC Let the straight likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F PROBLEM produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle right angles segment semicircle shown side BC sides square of AC straight line AC Take touches the circle triangle ABC twice the rectangle wherefore whole