## New Elementary Geometry: With Practical Applications : a Shorter Course Upon the Basis of the Larger Work |

### From inside the book

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**semicircle**. THEOREM II . 141. In the same circle , or in equal circles , equal arcs are subtended by equal chords ...**semicircle**AD B may be applied to the D BE G F**semicircle**EGF ; and the curve line ADB will coincide with the curve ... Page 48

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**semicircle**ADB be applied to its equal EGF , with the radius AC on its cqual E O , since the angles ACD , E OG are equal , the radius CD will fall on O G , and the point D on G. Therefore the arcs AD and E G coincide with each other ... Page 56

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**semicircle**, is a right angle ; because it is measured by half the semi - circumference , BOD ; that is , by the fourth part of the whole circumference . 163. Cor . 3. Every angle , B AC , inscribed in a segment greater than a**semicircle**... Page 61

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**semicircle**, is a right angle ( Theo . X. Cor . 2 , Bk . III . ) . PROBLEM V. At a point in a given straight line to make an angle equal to a given angle Let A be the given point , A B the given line , and EFG the given angle . From the ... Page 66

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**semicircle**, is a right angle ( Theo . X. Cor . 2 , Bk . III . ) ; there- fore A B is perpendicular to the radius CA at its extremity , A , and consequently is a tangent ( Theo . VII . Bk . III . ) . In like manner it be shown that E B ...### Other editions - View all

### Common terms and phrases

ABCD ABCDEF alti altitude Theo angle A CD axis base multiplied bisect chord circum circumference circumscribed cone convex surface D E F diagonal diameter divided ELEMENTARY ALGEBRA ellipse entire surface equal Theo equivalent formed frustum greater GREENLEAF'S half the sum hence homologous homologous sides hypothenuse inches inscribed circle inscribed square intersection magnitudes mean proportional measured by half Metric System number of sides parallelogram parallelopipedon perimeter perpendicular prism PROBLEM quadrilateral radii radius ratio rectangle rectangular regular polygon Required the area Required the volume rhombus right angles Theo right pyramid rods Scholium SCHOOLS sector semicircle side A B side B C similar slant hight solid sphere is equal spherical square described square feet square root tangent THEOREM third triangles A B C triangular triangular prism tude vertex

### Popular passages

Page 23 - 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 83 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar.

Page 29 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 61 - At a point in a given straight line to make an angle equal to a given angle.

Page 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 93 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.

Page 62 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.

Page 100 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...

Page 88 - FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.

Page 124 - But the solidity of each triangular prism is equal to the product of its base by its altitude ; and.