Elements of Geometry |
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Page 46
... direction are in the same sense , is called a convex polygon . If the changes of direction are not all in the same sense , the polygon is said to be re - entrant . 41. THEOREM . polygon is 360 ° . The sum 46 ELEMENTS OF GEOMETRY . 6 6.
... direction are in the same sense , is called a convex polygon . If the changes of direction are not all in the same sense , the polygon is said to be re - entrant . 41. THEOREM . polygon is 360 ° . The sum 46 ELEMENTS OF GEOMETRY . 6 6.
Page 47
... convex polygon as repre- sented in the accompanying figure we take any point . as ( S ) , and traverse the perimeter , starting in the direction indicated , and re- turning to ( S ) , we shall at the vertices , A , B , C , D , and E ...
... convex polygon as repre- sented in the accompanying figure we take any point . as ( S ) , and traverse the perimeter , starting in the direction indicated , and re- turning to ( S ) , we shall at the vertices , A , B , C , D , and E ...
Page 60
... measured by the half - sum of the intercepted arcs , the arc that is convex toward the point E , being negative , and the one concave toward E being positive . If the secant be further moved until it becomes a 60 ELEMENTS OF GEOMETRY .
... measured by the half - sum of the intercepted arcs , the arc that is convex toward the point E , being negative , and the one concave toward E being positive . If the secant be further moved until it becomes a 60 ELEMENTS OF GEOMETRY .
Page 115
... convex arcs will equal a2 . But the difference of the distances from P to the concave and convex arcs must be a ; since one of the distances is to be x and the other is to be x + a . P K а Q FIG . 156 . H If the constructed circle have ...
... convex arcs will equal a2 . But the difference of the distances from P to the concave and convex arcs must be a ; since one of the distances is to be x and the other is to be x + a . P K а Q FIG . 156 . H If the constructed circle have ...
Page 163
... convex , and it be desired to have one side of the triangle in the line of one side of the polygon , as AF : * NOTE . - Any tree ( not on the outer boundary ) will be the centre of a square , each vertex of which will be 20 feet from ...
... convex , and it be desired to have one side of the triangle in the line of one side of the polygon , as AF : * NOTE . - Any tree ( not on the outer boundary ) will be the centre of a square , each vertex of which will be 20 feet from ...
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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.