Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page 36
George Cunningham Edwards. Hypothenuse , which is the side opposite a right angle . Altitude , which is the perpendicular from vertex to base . 30. THEOREM . If at the middle of a side of an equi- lateral triangle a perpendicular be ...
George Cunningham Edwards. Hypothenuse , which is the side opposite a right angle . Altitude , which is the perpendicular from vertex to base . 30. THEOREM . If at the middle of a side of an equi- lateral triangle a perpendicular be ...
Page 71
... altitude . Sometimes this parallel is called the upper base . The rectangle is accurately described by bh or hb . In general , b and h are incommensurable with any assumed unit of length , and the area bh is incommensu- rable with the ...
... altitude . Sometimes this parallel is called the upper base . The rectangle is accurately described by bh or hb . In general , b and h are incommensurable with any assumed unit of length , and the area bh is incommensu- rable with the ...
Page 73
... altitudes . F Ih b L E n ' b ' H FIG . 91 . K If h and h ' happen to be equal , A A ' = b b i.e. when the altitudes are equal , the ratio of the areas is the same as the ratio of the bases . If instead of h and h ' being equal , it ...
... altitudes . F Ih b L E n ' b ' H FIG . 91 . K If h and h ' happen to be equal , A A ' = b b i.e. when the altitudes are equal , the ratio of the areas is the same as the ratio of the bases . If instead of h and h ' being equal , it ...
Page 74
... altitudes . 2. If the altitudes are equal , the surfaces will have the same ratio as the bases . 3. Show that if ... altitude . Therefore , b FIG . 93 . The surface of a triangle will be represented by bh · 2 Exercises . 1. Show that ...
... altitudes . 2. If the altitudes are equal , the surfaces will have the same ratio as the bases . 3. Show that if ... altitude . Therefore , b FIG . 93 . The surface of a triangle will be represented by bh · 2 Exercises . 1. Show that ...
Page 75
... altitudes . 2. Show that if their bases are equal , the surfaces will be to each other as their altitudes . 3. Show ... altitude ( h ) ; hence , Area ABC : = BC . h . Q. E. D. But Area ACDAD . h . ABC + ACD = 1⁄2 ( BC ) · h + 1⁄2 ( AD ) ...
... altitudes . 2. Show that if their bases are equal , the surfaces will be to each other as their altitudes . 3. Show ... altitude ( h ) ; hence , Area ABC : = BC . h . Q. E. D. But Area ACDAD . h . ABC + ACD = 1⁄2 ( BC ) · h + 1⁄2 ( AD ) ...
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Common terms and phrases
altitude angle bisector apothem auxiliary line axiom axis base bisect called centre changes of direction chord circumference coincide complete rotation congruent construct convex corresponding lines curve cylinder decagon determine diagonals diameter dicular diedral distance ellipse equal angles equally distant figure Find the locus fixed point frustum Geometry given circle given line given point greater hyperbola hypothenuse infinite number inscribed polygon interior angles isosceles joining lines be drawn lines forming Lune middle point NOTE number of sides oblique parabola parallelogram parallelopiped pass perimeter perpen perpendicular bisector Plane Geometry point of intersection position prism PROBLEM pyramid Q. E. D. Exercises quadrangle radii radius ratio rectangle regular polygon relations represent right angle right circular cone right triangle secant plane Show side opposite sphere spherical triangle square subtended surface THEOREM three sides triangular prism triedral vertex vertices volume
Popular passages
Page 25 - 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 26 - If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other, each to each, the other homologous parts are also equal, and the triangles are equal.
Page 17 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.
Page 293 - SUITABLE FOR USE IN PREPARATORY SCHOOLS. SELECTED FROM THE LISTS OF THE MACMILLAN COMPANY, Publishers. ARITHMETIC FOR SCHOOLS. By JB LOCK, Author of " Trigonometry for Beginners" "Elementary Trigonometry" etc Edited and Arranged for American Schools By CHARLOTTE ANGAS SCOTT, D.SC., Head of Math.
Page 172 - Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from the third.
Page 172 - Find the equation of the locus of a point which moves so that the sum of the squares of its distances from the x- and z-axes equals 4.
Page 100 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.