Elements of Euclid Adapted to Modern Methods in GeometryWilliam Collins, Sons,, 1874 - 216 sider |
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Side 12
... length or sum of the sides of a right lined figure is called the perimeter of the figure . The amount of surface contained ... rectangle is a parallelogram which has a right 12 EUCLID'S ELEMENTS .
... length or sum of the sides of a right lined figure is called the perimeter of the figure . The amount of surface contained ... rectangle is a parallelogram which has a right 12 EUCLID'S ELEMENTS .
Side 13
... contained by any two adjacent sides . This name is an abbreviation for " rectangular parallelogram . " It might have ... rectangle . 28. A square is a rectangle whose two adjacent sides are equal . 29. A rhombus is a parallelogram whose ...
... contained by any two adjacent sides . This name is an abbreviation for " rectangular parallelogram . " It might have ... rectangle . 28. A square is a rectangle whose two adjacent sides are equal . 29. A rhombus is a parallelogram whose ...
Side 44
... rectangle are therefore all right angles ( def . 27 ) . Cor . 3. - If two parallelograms have an angle of the one equal to an angle of the other , and the sides containing ... contain an angle which is either equal or supplemental . Thus if ...
... rectangle are therefore all right angles ( def . 27 ) . Cor . 3. - If two parallelograms have an angle of the one equal to an angle of the other , and the sides containing ... contain an angle which is either equal or supplemental . Thus if ...
Side 59
... rectangle BL is equal to the rectangle FM . But FM exceeds the square BG by the rectangle GM ; that is , by the rectangle contained by GA and AM , or by BA and the projection upon it of AC . ( I. 4. ) ( Ax . 6. ) ( Def . 27. ) ( Def ...
... rectangle BL is equal to the rectangle FM . But FM exceeds the square BG by the rectangle GM ; that is , by the rectangle contained by GA and AM , or by BA and the projection upon it of AC . ( I. 4. ) ( Ax . 6. ) ( Def . 27. ) ( Def ...
Side 60
... contained angle FBC ; ( Def . 28. ) ( Def . 28. ) ( Def . 8 and Ax . 2. ) ( I. 4. ) ( Ax . 6. ) therefore the triangle ABD is equal in area to FBC ; and their doubles are equal ; that is , the rectangle BL is equal to the rectangle FM ...
... contained angle FBC ; ( Def . 28. ) ( Def . 28. ) ( Def . 8 and Ax . 2. ) ( I. 4. ) ( Ax . 6. ) therefore the triangle ABD is equal in area to FBC ; and their doubles are equal ; that is , the rectangle BL is equal to the rectangle FM ...
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Elements of Euclid Adapted to Modern Methods in Geometry Euclid,James Bryce,David Munn (F.R.S.E.) Ingen forhåndsvisning - 1874 |
Almindelige termer og sætninger
AC and CB altitude angle AOB BA and AC bisecting the angle centre chord circles touch circumference cloth coincide Const conv Cor.-Hence diagonal diameter divided draw equal angles equal to BC equal to twice equiangular equilateral triangle Euclid exterior angle Fcap GEOGRAPHY geometrical given circle given line given point given straight line greater half the perimeter Hence hypotenuse inscribed intersecting isosceles triangle less Let ABC LL.D meet middle point multiple opposite sides parallel to BC parallelogram perpendicular polygon produced Proposition Q. E. D. Cor Q. E. D. PROP radius ratio rectangle contained rectilineal figure reflex angle remaining angles required to prove right angles right-angled triangle schol segments shew shewn side BC square on AC tangent THEOREM triangle ABC twice the rectangle twice the square whole line
Populære passager
Side 68 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Side 77 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 50 - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram is double of the triangle.
Side 87 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section.
Side 30 - Any two sides of a triangle are together greater than the third side.
Side 204 - Tin; rectangle, contained by the diagonals of a quadrilateral inscribed in a circle, is equal to the sum of the rectangles contained by its opposite sides. Let ABCD be any quadrilateral inscribed in a circle...
Side 89 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Side 98 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.