Elements of Geometry |
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Page x
... limit Limit axioms Area of a circle . PROBLEMS 117 · 121 124 126 137 Intersections of planes Perpendiculars to planes CHAPTER IX . Parallels X CONTENTS .
... limit Limit axioms Area of a circle . PROBLEMS 117 · 121 124 126 137 Intersections of planes Perpendiculars to planes CHAPTER IX . Parallels X CONTENTS .
Page xviii
... limit . While the beginnings are based upon definitions and axioms , it does not follow that all of the definitions and axioms are to be brought forward at the opening of the subject . As the information of the student grows , new ...
... limit . While the beginnings are based upon definitions and axioms , it does not follow that all of the definitions and axioms are to be brought forward at the opening of the subject . As the information of the student grows , new ...
Page 20
... limits of the drawing . Hint . - Draw an auxiliary line connecting two points of inter- section and then apply Ex . 1. Two applications will be necessary . 3. Establish the theorem when the third and fourth lines intersect between the ...
... limits of the drawing . Hint . - Draw an auxiliary line connecting two points of inter- section and then apply Ex . 1. Two applications will be necessary . 3. Establish the theorem when the third and fourth lines intersect between the ...
Page 52
... limit toward which the secant approaches as the points of intersection approach coincidence . A point being position and not having magnitude , B may pass through and beyond the position A. When that happens , the rotating line will ...
... limit toward which the secant approaches as the points of intersection approach coincidence . A point being position and not having magnitude , B may pass through and beyond the position A. When that happens , the rotating line will ...
Page 70
... at each step we should come nearer the point . is said to be the LIMIT toward which we approach as we increase the number of decimal places in .6666 ..... 57. We know from § 19 that parallel lines are 70 ELEMENTS OF GEOMETRY .
... at each step we should come nearer the point . is said to be the LIMIT toward which we approach as we increase the number of decimal places in .6666 ..... 57. We know from § 19 that parallel lines are 70 ELEMENTS OF GEOMETRY .
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Common terms and phrases
AB² altitude Analysis apothem approach auxiliary line axis base bisect called centre chord circumference circumscribed polygon coincide cone convex convex polygon corresponding lines curve cylinder decagon determine diagonals diameter dicular diedral distance ellipse equally distant figure Find the locus fixed point frustum Geometry given circle given line given point given segment greater Hence hypothenuse inscribed polygon interior angles isosceles joining lines be drawn middle point move NOTE number of sides oblique parabola parallel parallelogram parallelopiped pass perimeter perpen perpendicular bisector point of intersection position prism PROBLEM pyramids Q. E. D. Exercises quadrangle radii radius ratio re-entrant polygon rectangle regular polygon represent right angles right circular cone right triangle rotation secant Show side opposite similar 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.