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

### From inside the book

Results 1-5 of 13

Page 30

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**homologous**angles are equal , and all**homologous**lines are proportional . Remark . Either of these conditions , however , is suf ficient to determine their similarity ; for by altering the angles , we alter the ratio of the sides and ... Page 31

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**homologous**lines proportional . 93. Remark . If diagonals were drawn through cor- responding vertices in the two polygons ; being homolo- gous dimensions , they would be proportional ; and being proportional , the triangles into which ... Page 59

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**homologous**lines are proportional in similar triangles , we have this general rule - Similar tri- angles are to each other as the second powers of their ho- mologous dimensions ; or , as the squares described upon their**homologous**lines ... Page 62

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**homologous**measures proportional . In the application of the elementary principles , these two propositions are continually used . 175. If b2 + c2 a2 , then b2 — a2 = a2 c2 , and c2 b2 ; that is , The square of one side of a right ... Page 78

... any two planes in the one , will be equal to the inclination of the

... any two planes in the one , will be equal to the inclination of the

**homologous**planes in the other . * This was formerly called a solid angle . 218. Remark 1. If the plane angles be unequal , 78 Elements of Geometry . 72-96.### Other editions - View all

### Common terms and phrases

ABCD allel axis base bisect body called centre chord circumference co-ordinate planes conical surface construct contained cutting plane cylinder cylindrical surface Descriptive Geometry determine diagonals diameter dicular diedral distance draw equivalent exterior angles faces figure four right-angles generatrix Geometry give given line ground line height homologous horizontal plane horizontal projection horizontal trace hypothenuse inclination inscribed polygon intersection isosceles triangle line parallel lunary surface magnitude meet multiplied number of sides opposite parallel lines parallelogram parallelopiped perpen perpendicular perspective plane angles plane of projection plane passing polyedral angle polyedrons PROBLEM projecting planes proposed plane proposed point pyramid radii ratio rectangle rectilinear regular polygons revolve right-angled triangle right-line similar triangles sphere square straight line summit Suppose surface of revolution tangent tetraedron tion triangle ABC triangular prism triedral angle vertex vertical plane vertical projection 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 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 13 - 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 65 - 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 61 - 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 12 - 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 63 - 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.

Page 24 - 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 62 - The rectangle contained by the sum and difference of two lines, is equivalent to the difference of the squares of those lines.

Page ii - States entitled an act for the encouragement of learning hy securing the copies of maps, charts and books to the author., and proprietors of such copies during the times therein mentioned, 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 times therein mentioned and extending the benefits thereof to the arts of designing, engraving and...