The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 pages |
From inside the book
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Page 7
... join CA ' are afterwards used as an abbreviation for ' draw a straight line from C to A. ' 2. If we join AD and BD ( D being the other point in which the two circles cut each other ) another equilateral triangle ADB will be described on ...
... join CA ' are afterwards used as an abbreviation for ' draw a straight line from C to A. ' 2. If we join AD and BD ( D being the other point in which the two circles cut each other ) another equilateral triangle ADB will be described on ...
Page 14
... join FC , GB . Because AF is equal to AG ( const . ) and AB to AC , [ I. 3 . [ HYP . the two sides FA , AC are equal to the two sides GA , AB , each to each , and they contain the angle FAG common to the two triangles AFC , AGB ...
... join FC , GB . Because AF is equal to AG ( const . ) and AB to AC , [ I. 3 . [ HYP . the two sides FA , AC are equal to the two sides GA , AB , each to each , and they contain the angle FAG common to the two triangles AFC , AGB ...
Page 18
... Join CD . In the case in which the vertex of each triangle is without the other triangle ; Because AC is equal to AD , [ HYP . therefore the angle ACD is equal to the angle ADC ; [ I. 5 . But the angle ACD is greater than the angle BCD ...
... Join CD . In the case in which the vertex of each triangle is without the other triangle ; Because AC is equal to AD , [ HYP . therefore the angle ACD is equal to the angle ADC ; [ I. 5 . But the angle ACD is greater than the angle BCD ...
Page 21
... join AD , BD , and prove that the angles CAB , DAB are equal to each other . Ex . 4. - In the figure of Prop .. I join CD and prove that the angles ACD , BCD are equal to each other . Ex . 5. - In the figure of Prop . I let E be the ...
... join AD , BD , and prove that the angles CAB , DAB are equal to each other . Ex . 4. - In the figure of Prop .. I join CD and prove that the angles ACD , BCD are equal to each other . Ex . 5. - In the figure of Prop . I let E be the ...
Page 22
... Join DE . [ I. 3 . Upon DE , on the side remote from A , describe the equilateral A DEF . Join AF . The straight line AF shall bisect △ BAC . In the two As FAD , FAE AD = AE , [ I. I. AF is common , [ CONST . .. ¿ DAF LEAF . [ DEF . 24 ...
... Join DE . [ I. 3 . Upon DE , on the side remote from A , describe the equilateral A DEF . Join AF . The straight line AF shall bisect △ BAC . In the two As FAD , FAE AD = AE , [ I. I. AF is common , [ CONST . .. ¿ DAF LEAF . [ DEF . 24 ...
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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...