The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 páginas |
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Página 9
... shown that AL is equal to BG ; therefore AL is equal to BC . [ AX . 3 . [ DEF . 15 . [ AX . I. NOTES . I. ( a ) The point A may be joined with either end of the line CB ; ( 6 ) The equilateral triangle described on this join as base may ...
... shown that AL is equal to BG ; therefore AL is equal to BC . [ AX . 3 . [ DEF . 15 . [ AX . I. NOTES . I. ( a ) The point A may be joined with either end of the line CB ; ( 6 ) The equilateral triangle described on this join as base may ...
Página 12
... on DF , because the angle BAC is equal to the angle EDF ; therefore also the point C will coincide with the point F , because AC is equal to DF ; [ HYP . [ HYP . But the point B was shown to coincide with the 12 Euclid's Elements .
... on DF , because the angle BAC is equal to the angle EDF ; therefore also the point C will coincide with the point F , because AC is equal to DF ; [ HYP . [ HYP . But the point B was shown to coincide with the 12 Euclid's Elements .
Página 13
... shown to coincide with the point E ; therefore the base BC will coincide with the base EF , for if not , two straight lines would enclose a space , which is impossible ; [ AX . 10 . therefore the base BC is equal to the base EF ; [ AX ...
... shown to coincide with the point E ; therefore the base BC will coincide with the base EF , for if not , two straight lines would enclose a space , which is impossible ; [ AX . 10 . therefore the base BC is equal to the base EF ; [ AX ...
Página 15
... shown to be equal to GB , [ AX . 3 . and the angle BFC ( contained by BF , FC ) to the angle CGB ( contained by CG , GB ) ; therefore the angle CBF is equal to the angle BCG , and the angle BCF is equal to the angle CBG . · [ I . 4 ...
... shown to be equal to GB , [ AX . 3 . and the angle BFC ( contained by BF , FC ) to the angle CGB ( contained by CG , GB ) ; therefore the angle CBF is equal to the angle BCG , and the angle BCF is equal to the angle CBG . · [ I . 4 ...
Página 19
... shown by AB'C'D without having to stretch or compress any of the bars of which it is composed . But if a fifth bar , EF , were pivoted to A D AB , AD at E and F , it would be impossible for the distortion indicated in the figure to take ...
... shown by AB'C'D without having to stretch or compress any of the bars of which it is composed . But if a fifth bar , EF , were pivoted to A D AB , AD at E and F , it would be impossible for the distortion indicated in the figure to take ...
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...