The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's edCassell, Petter and Galpin, 1881 - 212 páginas |
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Página 30
... similar reason , EF is equal to BC . Therefore AD is equal ( 4x . 1 ) to EF ; and DE is common to both . Wherefore the whole , or the re- mainder A E , is equal to the whole , or the remainder DF ( Ar . 2 or 3 ) ; and AB is equal ( I ...
... similar reason , EF is equal to BC . Therefore AD is equal ( 4x . 1 ) to EF ; and DE is common to both . Wherefore the whole , or the re- mainder A E , is equal to the whole , or the remainder DF ( Ar . 2 or 3 ) ; and AB is equal ( I ...
Página 55
... Similar segments of circles are those in which the angles are equal , or which contain equal angles . AXIOMS I. If a point be taken between the centre of a circle and its circum ference , that point is within the circle ; and if a point ...
... Similar segments of circles are those in which the angles are equal , or which contain equal angles . AXIOMS I. If a point be taken between the centre of a circle and its circum ference , that point is within the circle ; and if a point ...
Página 63
... similar change on its enunciation as follows : -If two circles touch each other externally in any point , that point and the centres of the two circles are in the same straight line . This will form another exercise for the student ...
... similar change on its enunciation as follows : -If two circles touch each other externally in any point , that point and the centres of the two circles are in the same straight line . This will form another exercise for the student ...
Página 71
... similar ( Hyp . ) to the segment AD B , and similar segments of circles contain ( III . Def . 11 ) equal angles . Therefore the angle ACB is equal to the angle A D B ; that is , the exterior angle of the triangle A CD is equal to its ...
... similar ( Hyp . ) to the segment AD B , and similar segments of circles contain ( III . Def . 11 ) equal angles . Therefore the angle ACB is equal to the angle A D B ; that is , the exterior angle of the triangle A CD is equal to its ...
Página 73
... similar ( III . Def . 11 ) to the segment EDF , and they are upon equal straight lines BC and ÉF . But similar segments of circles upon equal straight lines , are equal ( III . 24 ) to one another . Therefore the segment BAC is equal to ...
... similar ( III . Def . 11 ) to the segment EDF , and they are upon equal straight lines BC and ÉF . But similar segments of circles upon equal straight lines , are equal ( III . 24 ) to one another . Therefore the segment BAC is equal to ...
Otras ediciones - Ver todas
The Elements of geometry; or, The first six books, with the eleventh and ... Euclides Vista completa - 1855 |
The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
A B and CD AC is equal adjacent angles altitude angle ABC angle ACB angle BAC angle EDF angle equal base BC bisected centre circle ABCD circumference common section cone Corollary cylinder described diameter draw equal angles equal Ax equal Const equal Hyp equiangular equimultiples Euclid exterior angle fore given rectilineal given straight line gnomon homologous inscribed join less Let the straight meet multiple opposite angle parallel parallelogram parallelopiped pentagon perpendicular polygon prism produced proposition Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD sphere squares of AC straight line drawn straight lines A B THEOREM third three plane angles three straight lines touches the circle triangle ABC triplicate ratio twice the rectangle vertex Wherefore
Pasajes populares
Página 21 - If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz.
Página 41 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 2 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Página 93 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Página 25 - 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 126 - 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 93 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater.
Página 40 - 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.
Página 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Página 19 - THEOREM. IF two triangles have two sides of the one equal to two sides of the...