The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 pages |
From inside the book
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Page 11
... theorems mentioned , to pass on in the way just suggested . After practice in the easier demonstrations which follow , they will be better able to grapple with the ... THEOREM . If two triangles have two sides Book I. Prop . 3 . II.
... theorems mentioned , to pass on in the way just suggested . After practice in the easier demonstrations which follow , they will be better able to grapple with the ... THEOREM . If two triangles have two sides Book I. Prop . 3 . II.
Page 14
... THEOREM . The angles at the base of an isosceles triangle are equal to one another , and , if the equal sides be produced , the angles on the other side of the base shall be equal to one another . Let ABC be an isosceles triangle ...
... THEOREM . The angles at the base of an isosceles triangle are equal to one another , and , if the equal sides be produced , the angles on the other side of the base shall be equal to one another . Let ABC be an isosceles triangle ...
Page 16
... THEOREM . If two angles of a triangle be equal , the sides also which sub- tend , or are opposite to the equal angles , shall be equal to one another . Let ABC be a triangle , having the angle ABC equal to the angle ACB : the side AC ...
... THEOREM . If two angles of a triangle be equal , the sides also which sub- tend , or are opposite to the equal angles , shall be equal to one another . Let ABC be a triangle , having the angle ABC equal to the angle ACB : the side AC ...
Page 17
... theorem consists of two parts , the hypothesis , or that which is assumed , and the conclusion , or that which is asserted to follow there- from . Two theorems are said to be converse , each of the other , when the hypothesis of each is ...
... theorem consists of two parts , the hypothesis , or that which is assumed , and the conclusion , or that which is asserted to follow there- from . Two theorems are said to be converse , each of the other , when the hypothesis of each is ...
Page 18
... THEOREM . On the same base and on the same side of it there cannot be two triangles having their sides , which are terminated in one extremity of the base equal to one another , and likewise those which are terminated at the other ...
... THEOREM . On the same base and on the same side of it there cannot be two triangles having their sides , which are terminated in one extremity of the base equal to one another , and likewise those which are terminated at the other ...
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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...