Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in an Appendix, the Theory of ProjectionBaldwin and Cradock, 1830 - 272 páginas |
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Página 14
... common to both , the remain- ing angle MBN is equal to ABC ( ax . 3. ) . Therefore , ( ax . 1. ) ABC is equal to H K L. Therefore , & c . Cor . The demonstration of the second case , viz . that in which the sides of the one angle are ...
... common to both , the remain- ing angle MBN is equal to ABC ( ax . 3. ) . Therefore , ( ax . 1. ) ABC is equal to H K L. Therefore , & c . Cor . The demonstration of the second case , viz . that in which the sides of the one angle are ...
Página 31
... common measure of the two may be found , i . e . a magnitude which is con- tained in each of them a certain number of times exactly . In like manner , any number of mag- For example , let A B C D , and II . § 1. ] 31 GEOMETRY BOOK II ...
... common measure of the two may be found , i . e . a magnitude which is con- tained in each of them a certain number of times exactly . In like manner , any number of mag- For example , let A B C D , and II . § 1. ] 31 GEOMETRY BOOK II ...
Página 32
... common measure , are said to be incommen- surable . Magnitudes A , B , which have one common measure M , have also many others , indeed , an unlimited number of common measures , for ( as will be shown in Prop . 1. ) every magnitude ...
... common measure , are said to be incommen- surable . Magnitudes A , B , which have one common measure M , have also many others , indeed , an unlimited number of common measures , for ( as will be shown in Prop . 1. ) every magnitude ...
Página 33
... common numerical ratio : and , in every case , if two magnitudes , and other two , have a common numerical ratio , the four magnitudes are , accord- ing to this definition , proportionals . It is evident from the observations on def . 6 ...
... common numerical ratio : and , in every case , if two magnitudes , and other two , have a common numerical ratio , the four magnitudes are , accord- ing to this definition , proportionals . It is evident from the observations on def . 6 ...
Página 34
... common factor , the same ratio may be expressed by any terms , as 5 : 6 , which are like parts of the given terms . For , if M be the common measure which is contained in A 10 × 5 times , and in B 10x 6 times , it is evident that 10 M ...
... common factor , the same ratio may be expressed by any terms , as 5 : 6 , which are like parts of the given terms . For , if M be the common measure which is contained in A 10 × 5 times , and in B 10x 6 times , it is evident that 10 M ...
Otras ediciones - Ver todas
Geometry, Plane, Solid, and Spherical, in Six Books: To Which Is Added, in ... Pierce Morton Sin vista previa disponible - 2023 |
Geometry, Plane, Solid, and Spherical, in Six Books: To Which Is Added, in ... Pierce Morton Sin vista previa disponible - 2013 |
Términos y frases comunes
A B C a² b² ABCD altitude asymptote axes axis base bisected centre chord circle circumference circumscribed co-ordinates common section conic section contained convex surface curve cylinder describe diameter difference dihedral angle distance divided draw drawn ellipse equal angles equation frustum given line given point given straight line gles greater hence hyperbola hypotenuse inscribed intersection join Latus Rectum less likewise locus magnitudes meet parabola parallel parallelogram parallelopiped pass pendicular perimeter perpendicular perspective projection pole prism produced projection PROP pyramid radii radius ratio rectangle rectangular rectilineal figure regular polygon right angles Scholium segment similar solid angles solid content sphere spherical angle spherical arc spherical triangle square tangent tion touch triangle ABC vertex vertical y₁
Pasajes populares
Página 196 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Página 64 - 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 20 - In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute angles ; and upon BC, one of the sides containing it, let fall the perpendicular...
Página 10 - 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 189 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Página 1 - 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 84 - The angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same part of the circumference.
Página 78 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Página 79 - EQUAL straight lines in a circle are equally distant from the centre ; and those which are equally distant from the centre, are equal to one another.
Página 264 - IF two straight lines cut one another, the vertical, or opposite, angles shall be equal.