The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 páginas |
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Página 5
... , are equal to one another . 9. The whole is greater than its part . 10. Two straight lines cannot enclose a space . II . All right angles are equal to one another . B DEF . - A triangle with its three sides equal Axioms . 5.
... , are equal to one another . 9. The whole is greater than its part . 10. Two straight lines cannot enclose a space . II . All right angles are equal to one another . B DEF . - A triangle with its three sides equal Axioms . 5.
Página 13
... whole triangle ABC coincides with the whole triangle DEF , and is equal to it . [ AX . 8 . Also since AB , BC coincide with DE , EF , therefore the angle B is equal to the angle E. [ AX . 8 . And since AC , CB coincide with DF , FE ...
... whole triangle ABC coincides with the whole triangle DEF , and is equal to it . [ AX . 8 . Also since AB , BC coincide with DE , EF , therefore the angle B is equal to the angle E. [ AX . 8 . And since AC , CB coincide with DF , FE ...
Página 14
... , AGB , therefore the base FC is equal to the base GB , the angle ACF is equal to the angle ABG , and the angle AFC is equal to the angle AGB . [ I. 4 . Again , because the whole AF is equal to the 14 Euclid's Elements .
... , AGB , therefore the base FC is equal to the base GB , the angle ACF is equal to the angle ABG , and the angle AFC is equal to the angle AGB . [ I. 4 . Again , because the whole AF is equal to the 14 Euclid's Elements .
Página 15
... whole AF is equal to the whole AG , [ CONST . [ HYP . and the part AB is equal to the part AC , therefore the remainder BF is equal to the remainder CG . Now , FC has been shown to be equal to GB , [ AX . 3 . and the angle BFC ...
... whole AF is equal to the whole AG , [ CONST . [ HYP . and the part AB is equal to the part AC , therefore the remainder BF is equal to the remainder CG . Now , FC has been shown to be equal to GB , [ AX . 3 . and the angle BFC ...
Página 49
... whole △ DEF coincides with the whole A ABC and = it , and AB = DE , and AC = DF , Book I. Prop . 26 . 49.
... whole △ DEF coincides with the whole A ABC and = it , and AB = DE , and AC = DF , Book I. Prop . 26 . 49.
Otras ediciones - Ver todas
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...