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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Página 14
The straight line AB is divided into two equal parts in the point D. Which was to be done . PROP . XI . - PROBLEM . To draw a straight line at right angles to a given straight line , from a given point in the same .
The straight line AB is divided into two equal parts in the point D. Which was to be done . PROP . XI . - PROBLEM . To draw a straight line at right angles to a given straight line , from a given point in the same .
Página 32
E A For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And by the preceding proposition , ali the angles of ...
E A For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And by the preceding proposition , ali the angles of ...
Página 47
If there be two straight lines , one of which is divided into any number of parts , the rectangle contained by the two straight lines , is equal to the rectangles contained by the undivided line , and the several parts of the divided ...
If there be two straight lines , one of which is divided into any number of parts , the rectangle contained by the two straight lines , is equal to the rectangles contained by the undivided line , and the several parts of the divided ...
Página 48
If a straight line be divided into any two parts , the rectangles contained by the whole and each of the parts are together equal to the square of the whole line . Let the straight line AB be divided into any two parts in the point C ...
If a straight line be divided into any two parts , the rectangles contained by the whole and each of the parts are together equal to the square of the whole line . Let the straight line AB be divided into any two parts in the point C ...
Página 49
If a straight line be divided into any two parts , the rectangle contained by the whole and one of the parts is equal to the rectangle contained by the two parts , together with the square of the aforesaid part .
If a straight line be divided into any two parts , the rectangle contained by the whole and one of the parts is equal to the rectangle contained by the two parts , together with the square of the aforesaid part .
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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