The Harpur Euclid: An Edition of Euclid's ElementsRivingtons, 1890 - 515 sider |
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Side 156
... . 228. - ABCD is a square whose diagonals intersect in O ; AC is produced to E , so that CE is equal to AB ; prove that the square on AE is double the square on OE . Ex . 229. - Divide a line internally or externally 156 Euclid's Elements .
... . 228. - ABCD is a square whose diagonals intersect in O ; AC is produced to E , so that CE is equal to AB ; prove that the square on AE is double the square on OE . Ex . 229. - Divide a line internally or externally 156 Euclid's Elements .
Side 157
... internally or externally into two parts such that the difference between their squares shall be equal to a given square . Ex . 230. — If AB is divided at C so that the square on AC is double the square on CB , the sum of AB and CB will ...
... internally or externally into two parts such that the difference between their squares shall be equal to a given square . Ex . 230. — If AB is divided at C so that the square on AC is double the square on CB , the sum of AB and CB will ...
Side 172
... internally . PROPOSITION 6 . If two circles touch one another internally 172 Euclid's Elements .
... internally . PROPOSITION 6 . If two circles touch one another internally 172 Euclid's Elements .
Side 173
... internally they shall not have the same centre . Let the Os ABC , CDE touch one another internally at C , they shall not have the same centre . A D E B Find F , the centre of the inner OCDE ; join FC , draw FE any other radius of CDE ...
... internally they shall not have the same centre . Let the Os ABC , CDE touch one another internally at C , they shall not have the same centre . A D E B Find F , the centre of the inner OCDE ; join FC , draw FE any other radius of CDE ...
Side 180
... join KA , KB , KC . Then rad . KA = rad . KB = rad . KC , .. K is the centre of the other O , which is impossible . [ III . 9 . [ III . 5 . PROPOSITION 11 . If two circles touch each other internally 180 Euclid's Elements .
... join KA , KB , KC . Then rad . KA = rad . KB = rad . KC , .. K is the centre of the other O , which is impossible . [ III . 9 . [ III . 5 . PROPOSITION 11 . If two circles touch each other internally 180 Euclid's Elements .
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The Harper Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Euclid,Edward Mann Langley,W. Seys Phillips Uten tilgangsbegrensning - 1890 |
The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Euclid,Edward Mann Langley,W. Seys Phillips Uten tilgangsbegrensning - 1894 |
The Harpur Euclid: An Edition of Euclid's Elements, Revised in Accordance ... Edward Mann Langley,Euclid,W. Seys Phillips Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 390 - ... figures are to one another in the duplicate ratio of their homologous sides.
Side 97 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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.
Side 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.
Side 40 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 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.
Side 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...