## Elements of Geometry Upon the Inductive Method: To which is Added an Introduction to Descriptive Geometry |

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angle axis base body called centre chord circle circumference circumscribed common cone consequently considered construct contained corresponding curve cylinder described determine diameter difference direction distance divide draw drawn edges elements entire equal equivalent evident expressed faces feet figure follows four Geometry give given given line greater ground line half height horizontal horizontal plane horizontal projection inclination increase inscribed intersection less magnitude mean measure meet method multiplied opposite parallel parallelogram parallelopiped passing perpendicular perspective picture polygon portion position prism PROBLEM projection proportion proposed proposition pyramid radii radius ratio rectangle regular remaining Remark represent respectively result revolve right-angles sides similar space sphere spherical square straight line Suppose surface tangent third tion trace triangle triedral angle truth vertex vertical vertical plane volume

### 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 xvi - 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 ii - 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 times therein mentioned,* and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints.

Page xvii - FGH, have a side and the two adjacent angles of the one equal to a side and the two adjacent angles of the other, each to each ; therefore these triangles are equal (Prop.

Page 51 - 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 47 - The square described upon the hypothenuse of a rightangled triangle is equivalent to the sum of the squares described upon the other two sides.

Page xi - The circumference of every circle is supposed to' be divided into 360 equal parts, called degrees ; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.

Page 10 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.

Page ii - CLERK'S OFFIcE. BE it remembered, that on the eleventh day of November, AD 1830, in the fiftyfifth year of the Independence of the United States of America, Gray & Bowen, of the said district, have deposited in this office the title of a book, the right whereof...

Page 49 - Prove that in any triangle the square on the side opposite an acute angle is equivalent to the sum of the squares of the other two sides diminished by twice the product of one of these sides and the projection of the other upon that side.