The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 pages |
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... Pass Examinations in Geometry , in so far as that no axioms other than those of Euclid shall be admitted , and that no proof of a proposition be allowed which assumes the truth of any pro- position which does not precede it according to ...
... Pass Examinations in Geometry , in so far as that no axioms other than those of Euclid shall be admitted , and that no proof of a proposition be allowed which assumes the truth of any pro- position which does not precede it according to ...
Page 11
... pass on in the way just suggested . After practice in the easier demonstrations which follow , they will be better able to grapple with the difficulties with which they were previously unable to cope . PROPOSITION 4. THEOREM . If two ...
... pass on in the way just suggested . After practice in the easier demonstrations which follow , they will be better able to grapple with the difficulties with which they were previously unable to cope . PROPOSITION 4. THEOREM . If two ...
Page 46
... passes through F we have at once EG > EF . [ I. 23 . [ I. 3 . If EG does not pass through F , bisect FDG by the straight . line DH , meeting EG in H ; join HF . [ I. 9 . Then in As FDH , GDH FD , DH = GD , DH , and FDH = ... HF = HG ...
... passes through F we have at once EG > EF . [ I. 23 . [ I. 3 . If EG does not pass through F , bisect FDG by the straight . line DH , meeting EG in H ; join HF . [ I. 9 . Then in As FDH , GDH FD , DH = GD , DH , and FDH = ... HF = HG ...
Page 55
... passing through a given point is also spoken of as a pencil . All the straight lines which satisfy the same geometrical condition are spoken of as a set . See Henrici ( Congruent Figures , pp . 137-146 . ) Thus Ex . 39 , 41 , 42 might ...
... passing through a given point is also spoken of as a pencil . All the straight lines which satisfy the same geometrical condition are spoken of as a set . See Henrici ( Congruent Figures , pp . 137-146 . ) Thus Ex . 39 , 41 , 42 might ...
Page 57
... pass through the given point . ( See Ex . 45. ) ( ii . ) .— Through a given point draw as many st . lines as you can , making equals with two given intersecting st . lines . The required straight lines are those particular members of a ...
... pass through the given point . ( See Ex . 45. ) ( ii . ) .— Through a given point draw as many st . lines as you can , making equals with two given intersecting st . lines . The required straight lines are those particular members of a ...
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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...