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 40
Let ABCD be a parallelogram , of which the diameter is AC , and EH , FG , the parallelograms about AC , that is , through which AC passes , and BK , KD , the other parallelograms which make up the whole figure ABCD , which are therefore ...
Let ABCD be a parallelogram , of which the diameter is AC , and EH , FG , the parallelograms about AC , that is , through which AC passes , and BK , KD , the other parallelograms which make up the whole figure ABCD , which are therefore ...
Σελίδα 67
If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre , it shall cut it at right angles ; and conversely , if it cut it at right angles , it shall bisect it .
If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre , it shall cut it at right angles ; and conversely , if it cut it at right angles , it shall bisect it .
Σελίδα 68
Each of the angles AFE , BFE , is a right angle ; wherefore the straight line CD , drawn through the centre , bisecting another AB that does not pass through the centre , cuts the same at right angles . But let CD cut AB at right angles ...
Each of the angles AFE , BFE , is a right angle ; wherefore the straight line CD , drawn through the centre , bisecting another AB that does not pass through the centre , cuts the same at right angles . But let CD cut AB at right angles ...
Σελίδα 69
bisects another AC which does not pass through the centre , it shall cut it ( III . 3. ) at right angles ; wherefore 1 . FEA is a right angle . Again , because the straight line FE bisects the straight line BD which does not pass ...
bisects another AC which does not pass through the centre , it shall cut it ( III . 3. ) at right angles ; wherefore 1 . FEA is a right angle . Again , because the straight line FE bisects the straight line BD which does not pass ...
Σελίδα 70
... nearer to the line which passes through the centre is always greater than one more remote : and from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line .
... nearer to the line which passes through the centre is always greater than one more remote : and from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line .
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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