The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With the Elements of Plane Trigonometry, and an Appendix in Four Books : With Notes and IllustrationsLongmans, Green, 1845 - 352 páginas |
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Página 7
... triangle on a given finite straight line . † Let AB be the given straight line : it is required to describe an ... ABC is the equilateral triangle required . D B Because the point A is the centre of the circle BCD , AC is equal ( I ...
... triangle on a given finite straight line . † Let AB be the given straight line : it is required to describe an ... ABC is the equilateral triangle required . D B Because the point A is the centre of the circle BCD , AC is equal ( I ...
Página 10
... triangle ABC to the triangle DEF ; and ( 3 ) the other angles , to which the equal sides are opposite , are equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . B A E C P H For , if the triangle ABC ...
... triangle ABC to the triangle DEF ; and ( 3 ) the other angles , to which the equal sides are opposite , are equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . B A E C P H For , if the triangle ABC ...
Página 11
... ABC be an isosceles triangle , of which the side AB is equal to AC , and let the sides AB , AC be produced to D and E ; the angle ABC is equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE ...
... ABC be an isosceles triangle , of which the side AB is equal to AC , and let the sides AB , AC be produced to D and E ; the angle ABC is equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE ...
Página 12
... ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal to the side AC . D Λ For , if AB be not equal to AC , † one of them is greater than the other let AB be the greater , and from it cut off ( I. 3 ) ...
... ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal to the side AC . D Λ For , if AB be not equal to AC , † one of them is greater than the other let AB be the greater , and from it cut off ( I. 3 ) ...
Página 13
... triangles that have their sides which are terminated in one extremity of the base equal to one another , and likewise those which are terminated in the other extremity . If it be possible , let there be two triangles ABC , ABD , upon ...
... triangles that have their sides which are terminated in one extremity of the base equal to one another , and likewise those which are terminated in the other extremity . If it be possible , let there be two triangles ABC , ABD , upon ...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... James Thomson, gen,James Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained corollary cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB.-To produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol scholium segments semicircle sides similar solid angles square of AC straight line drawn tangent THEOR.-If third triangle ABC trigonometry triplicate ratio vertex vertical angle wherefore
Pasajes populares
Página 130 - 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 45 - 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 on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Página 2 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Página 50 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Página 38 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Página 7 - If two triangles have two sides of the one equal to two sides of the...
Página 27 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 27 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Página 15 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Página 36 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.