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A B C adding altitude apply base called centre chord circ circle circumference coincide common cone Consequently considered construction contain convex surface cube cylinder definition demonstrated described determine diameter difference direction distance divided draw drawn entire equal equivalent evident express faces fall feet figure formed frustum geometry given greater half height Hence homologous inches infinite inscribed length less manner mean measure meet middle multiplied namely number of sides object oblique parallel parallelogram parallelopiped pass perimeter perpendicular placed plane polygon position prism proportion proved pyramid radii radius ratio reasoning regular polygon remain respect right angles sector segment sides similar solidity sphere square straight line suppose taken term THEOREM.-The third tion triangle triangular true unit vertex vertices
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 48 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
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 ii - ... and also to an Act, entitled, " An Act- supplementary to an Act, entitled, ' An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies, during the limes therein mentioned ;' and extending the benefits thereof to the arts of designing, engraving, and etching historical, and other prints.
Page xiv - If a straight line meets 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 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 xiv - 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.
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 xiv - 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. 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another.