Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page vi
... length . The chapters have been divided into articles , and these have been numbered for convenience in cross - reference . But the student should refer to principles or facts by stating them in full . The writer thinks that the proper ...
... length . The chapters have been divided into articles , and these have been numbered for convenience in cross - reference . But the student should refer to principles or facts by stating them in full . The writer thinks that the proper ...
Page 4
... length , our representations of them are limited by the extent of the surface upon which our representations are made . Henceforth when the word line is used without any qualification a straight line is understood . 5. ROTATION AXIOM ...
... length , our representations of them are limited by the extent of the surface upon which our representations are made . Henceforth when the word line is used without any qualification a straight line is understood . 5. ROTATION AXIOM ...
Page 60
... length it is equal to the arc D'D ' , but under the circumstances is negative . Hence the angle CED " is measured by the half - sum of the intercepted arcs , the arc that is convex toward the point E , being negative , and the one ...
... length it is equal to the arc D'D ' , but under the circumstances is negative . Hence the angle CED " is measured by the half - sum of the intercepted arcs , the arc that is convex toward the point E , being negative , and the one ...
Page 62
... the arc subtended by the lesser chord throughout its entire length and extend beyond it . Hence it is greater , and the theorem is established . 53. THEOREM . The lesser of two unequal chords in 62 ELEMENTS OF GEOMETRY .
... the arc subtended by the lesser chord throughout its entire length and extend beyond it . Hence it is greater , and the theorem is established . 53. THEOREM . The lesser of two unequal chords in 62 ELEMENTS OF GEOMETRY .
Page 63
... length in a given circle are equally distant from the centre . 2. Find the maximum and minimum chords that may be drawn through a given point in a circle . 3. Establish the converse of the theorem . 4. Find the locus of any fixed point ...
... length in a given circle are equally distant from the centre . 2. Find the maximum and minimum chords that may be drawn through a given point in a circle . 3. Establish the converse of the theorem . 4. Find the locus of any fixed point ...
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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.