Elements of Geometry |
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Page vi
... greater number of relations ; and algebra may be of great service in conducting us to our conclusions by the readiest and most easy method . This work is divided into eight sections , four of which treat of plane geometry , and four of ...
... greater number of relations ; and algebra may be of great service in conducting us to our conclusions by the readiest and most easy method . This work is divided into eight sections , four of which treat of plane geometry , and four of ...
Page vii
... greater than any rectilineal figure of the same perimeter . The first section of the second part contains the properties of planes and of solid angles . This part is very necessary for the understanding of solids , and of figures in ...
... greater than any rectilineal figure of the same perimeter . The first section of the second part contains the properties of planes and of solid angles . This part is very necessary for the understanding of solids , and of figures in ...
Page ix
... to that represented by B , or A equal to B. A > B signifies that the magnitude represented by A exceeds that represented by B , or A greater than B. AB signifies A less than B. GEOM . b 2A , 3A , & c . , indicate double.
... to that represented by B , or A equal to B. A > B signifies that the magnitude represented by A exceeds that represented by B , or A greater than B. AB signifies A less than B. GEOM . b 2A , 3A , & c . , indicate double.
Page 2
... greater than a right angle , is an obtuse angle . 12. Two lines are said to be parallel ( fig . 5 ) , when , being situated in the same plane , and produced ever so far both ways , they do not meet . 13. A plane figure is a plane ...
... greater than a right angle , is an obtuse angle . 12. Two lines are said to be parallel ( fig . 5 ) , when , being situated in the same plane , and produced ever so far both ways , they do not meet . 13. A plane figure is a plane ...
Page 3
... greater than its part . 24. The whole is equal to the sum of all its parts . 25. Only one straight line can be drawn between two points . 26. Two magnitudes , whether they be lines , surfaces , or solids , are equal , when , being ...
... greater than its part . 24. The whole is equal to the sum of all its parts . 25. Only one straight line can be drawn between two points . 26. Two magnitudes , whether they be lines , surfaces , or solids , are equal , when , being ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle join less Let ABC let fall Let us suppose line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM third three angles triangle ABC triangular prism triangular pyramids vertex vertices whence
Popular passages
Page 67 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 9 - 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.
Page 65 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 160 - ABC (fig. 224) be any spherical triangle ; produce the sides AB, AC, till they meet again in D. The arcs ABD, ACD, will be...
Page 168 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Page 157 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 8 - Any side of a triangle is less than the sum of the other two sides...
Page 82 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 29 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Page 182 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.