Elements of Geometry |
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Page 43
... bases and equal altitudes , are equivalent . Demonstration . Let AB ( fig . 96 ) be the common base of the Fig . 96 . two parallelograms ABCD , ABEF ; since they are supposed to have the same altitude , the sides DC , FE , opposite to the ...
... bases and equal altitudes , are equivalent . Demonstration . Let AB ( fig . 96 ) be the common base of the Fig . 96 . two parallelograms ABCD , ABEF ; since they are supposed to have the same altitude , the sides DC , FE , opposite to the ...
Page 44
... ABCD , ABEF , which have the same base and the same altitude , are equivalent . 167. Corollary . Every parallelogram ABCD ( fig . 97 ) is equivalent to a rectangle of the same base and altitude . THEOREM . 168. Every triangle ABC ( fig ...
... ABCD , ABEF , which have the same base and the same altitude , are equivalent . 167. Corollary . Every parallelogram ABCD ( fig . 97 ) is equivalent to a rectangle of the same base and altitude . THEOREM . 168. Every triangle ABC ( fig ...
Page 46
... ABCD , AEHD , have the same altitude AD ; they are conse- quently to each other as their bases AB , AE . Likewise ... base by its altitude , provided that , by this product , we understand that of two numbers which are the num- ber of linear ...
... ABCD , AEHD , have the same altitude AD ; they are conse- quently to each other as their bases AB , AE . Likewise ... base by its altitude , provided that , by this product , we understand that of two numbers which are the num- ber of linear ...
Page 47
... ABCD . 175. Corollary . Parallelograms of the same base are to each other as their altitudes , and parallelograms of the same altitude are to each other as their bases ; for , A , B , C , being any three magnitudes whatever , we have ...
... ABCD . 175. Corollary . Parallelograms of the same base are to each other as their altitudes , and parallelograms of the same altitude are to each other as their bases ; for , A , B , C , being any three magnitudes whatever , we have ...
Page 48
... ABCD is equivalent to the parallelogram ADKL , and has for its measure EFX ... ABCD is equal to the product of the altitude EF by half the sum of the sides ... base AB , the point H will also be the middle of AD ; for the figure AHIL is ...
... ABCD is equivalent to the parallelogram ADKL , and has for its measure EFX ... ABCD is equal to the product of the altitude EF by half the sum of the sides ... base AB , the point H will also be the middle of AD ; for the figure AHIL is ...
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Common terms and phrases
ABC fig 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 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 triangle ABC triangular prism triangular pyramids vertex vertices whence
Popular passages
Page 65 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 21 - 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 - 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 63 - 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 22 - 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 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 80 - 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 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.
Page 24 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 153 - XVII.) ; hence two similar pyramids are to each other as the cubes of their homologous sides.