The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 páginas |
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Página 9
... side of that base ; ( c ) The other two sides of the equilateral triangle may be produced either both through the vertex , or , as in the diagram , both in the opposite direction ; so that with BC and A given there are eight ways in ...
... side of that base ; ( c ) The other two sides of the equilateral triangle may be produced either both through the vertex , or , as in the diagram , both in the opposite direction ; so that with BC and A given there are eight ways in ...
Página 12
... sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , namely AB to DE , and AC to DF , and the angle BAC equal to the angle EDF : the base BC shall be equal ...
... sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , namely AB to DE , and AC to DF , and the angle BAC equal to the angle EDF : the base BC shall be equal ...
Página 16
... 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 shall be equal to the side AB . A For if AC be not ...
... 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 shall be equal to the side AB . A For if AC be not ...
Página 21
... sides of the other , each to each , then the triangles are identically equal , and of the angles , those are equal which are opposite to equal sides . ( Syllabus . ) Ex . 3. - In the figure of Prop . I join AD , BD , and prove that the ...
... sides of the other , each to each , then the triangles are identically equal , and of the angles , those are equal which are opposite to equal sides . ( Syllabus . ) Ex . 3. - In the figure of Prop . I join AD , BD , and prove that the ...
Página 23
... side remote from A. 2. The demonstration would be just as easy if the △ DFE were merely an isosceles △ having DE ... opposite sides of a common base , AF , and such that superposition could be effected by turning either of them about ...
... side remote from A. 2. The demonstration would be just as easy if the △ DFE were merely an isosceles △ having DE ... opposite sides of a common base , AF , and such that superposition could be effected by turning either of them about ...
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The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Edward Mann Langley,Euclid,W. Seys Phillips Sin vista previa disponible - 2015 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
Página 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 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.
Página 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.
Página 40 - Any two sides of a triangle are together greater than the third side.
Página 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.
Página 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.
Página 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...