The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 pages |
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Page 24
... divided into two equal parts at the point D. In the two As ACD , BCD AC = CB , CD is common , and ACD 4 BCD , .. AD = DB . [ CONST . [ CONST . [ I. 4 . NOTE . The student should go through the successive steps 24 Euclid's Elements . Let ...
... divided into two equal parts at the point D. In the two As ACD , BCD AC = CB , CD is common , and ACD 4 BCD , .. AD = DB . [ CONST . [ CONST . [ I. 4 . NOTE . The student should go through the successive steps 24 Euclid's Elements . Let ...
Page 61
... divided into as many As as the figure has sides by drawing st . lines from a point F within the figure to each of its s . And by the preceding proposition all the Ls of these As = twice as many rt . 4s as there are As , i.e. as the ...
... divided into as many As as the figure has sides by drawing st . lines from a point F within the figure to each of its s . And by the preceding proposition all the Ls of these As = twice as many rt . 4s as there are As , i.e. as the ...
Page 67
... divided into congruent parts . Each is divided by lines || to the sides of the other . DEF . - The altitude of a figure , with reference to a given side as base , is the Lr distance between the base and the opposite side or vertex . Ex ...
... divided into congruent parts . Each is divided by lines || to the sides of the other . DEF . - The altitude of a figure , with reference to a given side as base , is the Lr distance between the base and the opposite side or vertex . Ex ...
Page 69
... divided into congruent parts in the way indicated in the diagram . Each is divided by lines parallel to the side of the other . 4 4 Ex . 71. State and prove a converse of this proposition . Ex . 72. - The locus of a point at a given ...
... divided into congruent parts in the way indicated in the diagram . Each is divided by lines parallel to the side of the other . 4 4 Ex . 71. State and prove a converse of this proposition . Ex . 72. - The locus of a point at a given ...
Page 100
... divided into equal parts , AB , BC , CD , DE , EF . O is any external point . a b A If OA , OB , OC , OD , OE , OF ( or these lines produced ) meet a straight line parallel to AF in a , b , c , d , e , f , show that ab , bc , cd , de ...
... divided into equal parts , AB , BC , CD , DE , EF . O is any external point . a b A If OA , OB , OC , OD , OE , OF ( or these lines produced ) meet a straight line parallel to AF in a , b , c , d , e , f , show that ab , bc , cd , de ...
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Common terms and phrases
bisect bisector Brocard point chord circum-circle of triangle circumference coincide common concyclic congruent cyclic quadrilateral demonstration described diagonals diameter diamr divided draw equal angles equiangr equiangular equidistant equilateral triangle equimultiples Euclid exterior angle Geometry given circle given point given ratio given st given straight line given triangle greater Hence inscribed intersect isosceles isosceles triangle Join Let ABC locus magnitude meet mid-point opposite sides parallel parallelogram pass pentagon perpendicular plane produced Prop PROPOSITION PROPOSITION 13 radical axis radius rect rectangle contained reqd rhombus right angles segment Show sides BC similar Similarly Simson's line square straight line drawn student subtended symmedian symmedian point tangent THEOREM touch triangle ABC vertex vertices
Popular passages
Page 21 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 369 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
Page 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 370 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Page 96 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 40 - Any two sides of a triangle are together greater than the third side.
Page 143 - Three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angles.
Page 407 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 156 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square...