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 ed1855 |
Dentro del libro
Resultados 1-5 de 77
Página 30
... similar reason , EF is equal to BC . Therefore AD is equal ( Ax . 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 ( Ax . 2 or 3 ) ; and AB is equal ( I ...
... similar reason , EF is equal to BC . Therefore AD is equal ( Ax . 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 ( Ax . 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 ...
... 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 ...
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 ADB , and similar segments of circles contain ( III . Def . 11 ) equal angles . Therefore the angle ACB is equal to the angle ADB ; that is , the exterior angle of the triangle A CD is equal to its ...
... similar ( Hyp . ) to the segment ADB , and similar segments of circles contain ( III . Def . 11 ) equal angles . Therefore the angle ACB is equal to the angle ADB ; 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 - 1881 |
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 C ABC is equal ABCD altitude angle ABC angle BAC base bisected Book centre circle circle ABC circumference common compounded cone Const contained Corollary cylinder definition demonstration described diameter divided double draw drawn equal angles equiangular equimultiples Exercise extremities fore four fourth given straight line greater half homologous inscribed join less magnitudes manner meet multiple opposite parallel parallelogram parallelopiped pass perpendicular plane polygon prism PROBLEM produced PROP proposition proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar similarly solid solid angle sphere square Take taken THEOREM third touch triangle ABC vertex Wherefore whole
Pasajes populares
Página 23 - 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 42 - 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 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 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 3 - 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.
Página 143 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Página 20 - PROBLEM. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.
Página 115 - Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes.
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...