## Elements of Geometry...: Translated from the French for the Use of the Students of the University at Cambridge, New England |

### From inside the book

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**faces**, the rectangle B will have for its absolute measure , that is , it will be equal to 4 superficial units . The more common and simple method is to take the square as the unit of surface ; and that square has been preferred , whose ... Page 117

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**faces**would , by being produced , cut the solid angle ; if it were other- wise , the sum of the plane angles would no longer be limited , and might be of any magnitude whatever . THEOREM . 359. If two solid angles are respectively ... Page 123

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**faces**of a poly- edron is called a side or edge of the polyedron . 367. A regular polyedron is one , all whose**faces**are equal regular polygons , and all whose solid angles are equal to each other . There are five polyedrons of this ... Page 124

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**faces**parallelograms , and is called a parallelopiped . A parallelopiped is rectangular , when all its**faces**are rect- angles . 374. Among rectangular parallelopipeds is distinguished the cube or regular hexaedron comprehended under six ... Page 125

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**face**or base of a polyedron , we can imagine the vertices of the different solid angles of the polye- drons ...**faces**and in part below it ; it is wholly on one side of this plane . THEOREM . 384. Two polyedrons cannot have the ...### Other editions - View all

Elements of Geometry...: Translated from the French for the Use of the ... No preview available - 2020 |

### Common terms and phrases

adjacent angles altitude angle ACB angle BAD angles equal base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom geometry gles greater hence homologous sides hypothenuse inclination inscribed circle intersection isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangular prism triangular pyramids vertex vertices whence

### 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 9 - 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 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.

Page 9 - Hence a straight line drawn from the vertex of an isosceles triangle, to the middle of the base, is perpendicular to that base, and divides the vertical angle into two equal parts.

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...

Page 61 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.

Page 166 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.

Page 153 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.

Page 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.

Page 164 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.