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

### From inside the book

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**Solid**, or Volume , is that which has length , breadth , and thickness . ANGLES AND LINES . 10. An Angle is the difference in the direction of two lines , which meet at a point ; as the angle A. The point of meeting , A , is the ver ... Page 122

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**solid**AG into 15 small paral- 7 lelopipedons , all equal to each other , hav- ing equal bases and equal altitudes ...**Solid**AG :**Solid**A L : : A E : A I. For , if this proportion is not correct , suppose we have :**Solid**A G**Solid**AL ... Page 124

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**Solid**A G :**Solid**A K :: ABCD : AM NO . But the two parallelopipedons A K , AZ , having the same base , AM NO , are to each other as their altitudes , A E , A X ( Theo . XII . ) ; hence we have "**Solid**A K :**Solid**A Z :: A E : A X ... Page 125

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**solid**, or volume , is called its volume , solidity , or**solid**contents . We assume as the unit of volume , or solidity , the cube , each of whose edges is the linear unit , and each of whose faces is the unit of surface . 300. Cor . 1 ... Page 132

... , by the plane FAC ; there will remain the

... , by the plane FAC ; there will remain the

**solid**A CDE - F , which may be considered as a quadrangular pyramid , whose vertex is F , and whose base is the parallelogram ACDE . Draw the diagonal 132 ELEMENTARY GEOMETRY .### 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.