Elements of Euclid Adapted to Modern Methods in GeometryWilliam Collins, Sons,, 1874 - 216 Seiten |
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Seite 12
... produced ever so far both ways , do not meet . Parallel lines are manifestly equidistant at all parts , and a moment's consideration will shew that two straight lines on different planes , although they are not parallel , may yet never ...
... produced ever so far both ways , do not meet . Parallel lines are manifestly equidistant at all parts , and a moment's consideration will shew that two straight lines on different planes , although they are not parallel , may yet never ...
Seite 14
... produced to any length in a straight line . 3. That a circle may be described from any centre , with a radius equal to any finite straight line . AXIOMS . 1. Things which are equal to the same , or to equals , are equal to one another ...
... produced to any length in a straight line . 3. That a circle may be described from any centre , with a radius equal to any finite straight line . AXIOMS . 1. Things which are equal to the same , or to equals , are equal to one another ...
Seite 18
... produced to equality with the greater ; and a line may be drawn equal to the sum of the two lines . These Propositions might have been omitted , as they are merely formal statements of the assumption which has been made , that distances ...
... produced to equality with the greater ; and a line may be drawn equal to the sum of the two lines . These Propositions might have been omitted , as they are merely formal statements of the assumption which has been made , that distances ...
Seite 20
... produced to G and H , the angles below the base shall also be equal . For , since AB and DE coincide , their ... produced . PROP . V. - THEOREM . The angles at the base of an isosceles triangle are equal , and if the equal sides be ...
... produced to G and H , the angles below the base shall also be equal . For , since AB and DE coincide , their ... produced . PROP . V. - THEOREM . The angles at the base of an isosceles triangle are equal , and if the equal sides be ...
Seite 21
... produced to D and E , the angles on the other side of the base are also equal , namely , the angle DBC equal to the angle ECB . In AB take any point F , and from AC cut off AG equal to AF ; join F , C , and B , G. Comparing the two ...
... produced to D and E , the angles on the other side of the base are also equal , namely , the angle DBC equal to the angle ECB . In AB take any point F , and from AC cut off AG equal to AF ; join F , C , and B , G. Comparing the two ...
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Elements of Euclid Adapted to Modern Methods in Geometry Euclid,James Bryce,David Munn (F.R.S.E.) Keine Leseprobe verfügbar - 1874 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 50 - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram is double of the triangle.
Seite 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.
Seite 30 - Any two sides of a triangle are together greater than the third side.
Seite 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...
Seite 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.
Seite 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.