Elements of Geometry: Containing the First Six Books of Euclid : with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added, Elements of Plane and Spherical TrigonometryW.E. Dean, 1849 - 317 páginas |
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Página 107
... fourth , equal to it , or less then the first of the magnitudes is said to have to the second the same ratio that the third has to the fourth . ; 6. Magnitudes are said to be proportionals , when the first has the same ratio to the ...
... fourth , equal to it , or less then the first of the magnitudes is said to have to the second the same ratio that the third has to the fourth . ; 6. Magnitudes are said to be proportionals , when the first has the same ratio to the ...
Página 108
... fourth ; or that the first is to the third as the second to the fourth : See Prop . 16 . of this Book . 15. Invertendo , by inversion : When there are four proportionals , and it is inferred , that the second is to the first , as the fourth ...
... fourth ; or that the first is to the third as the second to the fourth : See Prop . 16 . of this Book . 15. Invertendo , by inversion : When there are four proportionals , and it is inferred , that the second is to the first , as the fourth ...
Página 109
... fourth of the first rank , so is the third from the last , to the last but two , of the second rank ; and so on in a cross , or inverse , order ; and the inference is as in the 19th definition . It is demonstrated in the 23d Prop . of ...
... fourth of the first rank , so is the third from the last , to the last but two , of the second rank ; and so on in a cross , or inverse , order ; and the inference is as in the 19th definition . It is demonstrated in the 23d Prop . of ...
Página 111
... fourth , and if any equimultiples whatever be taken of the first and third , and any whatever of the second and fourth ; the multiple of the first shall have the same ratio to the multiple of the second , that the multiple of the third ...
... fourth , and if any equimultiples whatever be taken of the first and third , and any whatever of the second and fourth ; the multiple of the first shall have the same ratio to the multiple of the second , that the multiple of the third ...
Página 112
... fourth ; the first is to the second as the third to the fourth . First , if mA , mB be equimultiples of the magnitudes A and B , mA : A :: mB : B. Take of mA and B equimultiples by any number n ; and of A and B equimultiples by any ...
... fourth ; the first is to the second as the third to the fourth . First , if mA , mB be equimultiples of the magnitudes A and B , mA : A :: mB : B. Take of mA and B equimultiples by any number n ; and of A and B equimultiples by any ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder definition demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 149 - If the vertical angle of a triangle be bisected by a straight line which also cute the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 51 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Página 29 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Página 52 - 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 9 - 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 296 - 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 15 - UPON the same base, and on the same side of it, there cannot be two 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.
Página 283 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Página 22 - Any two sides of a triangle are together greater than the third side.
Página 26 - ... sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.