## Elements of Geometry: With Practical Applications, for the Use of Schools |

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A B fig adjacent angles angles are equal axis B A C base and altitude base multiplied bisect called centre chord circ circum circumference coincide convex surface cube cylinder D E F definition demonstrated diameter distance divided draw entire surface equally distant equivalent found by multiplying frustum Geometry given line Hence homologous sides hypothenuse inches infinite number infinitely small inscribed angles inscribed circle line A B linear unit mean proportional number of sides parallel sides parallelopiped pendicular perim perimeter perpendicular polyedrons preceding proposition proved pyramid radii radius regular polygon right angles right parallelogram right triangle semicircumference similar triangles solid angles sphere square feet straight line suppose tangent THEOREM THEOREM.-The tion trapezoid triangle A B C triangles are equal triangular prism vertex vertices

### Popular passages

Page ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...

Page xiv - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Page 63 - The square described on the hypotenuse of a right triangle is equivalent to the sum of the squares on the other two sides.

Page xv - LET it be granted that a straight line may be drawn from any one point to any other point.

Page 41 - In any proportion, the product of the means is equal to the product of the extremes.

Page 57 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.

Page xiv - If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another. 7. Things which are halves of the same are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.

Page 42 - Multiplying or dividing both the numerator and denominator of a fraction by the same number does not change the value of the fraction.

Page viii - Thus, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, was an experimental discovery, or why did the discoverer sacrifice a hecatomb when he made out its proof ?

Page 61 - THEOREM. The area of a trapezoid is equal to the product of its altitude, by half the sum of its parallel bases.