## Elements of Geometry and Conic Sections |

### From inside the book

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Page 57

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**Equivalent**figures are such as contain equal areas . Two figures may be**equivalent**, however dissimilar . Thus , a circle may be**equivalent**to a square , a triangle to a rec- tangle , & c . 3. Similar figures are such as have the angles ... Page 58

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**equivalent**. Let the parallelo- D grams ABCD , ABEF be placed so that their equal bases shall coin- C F ED F C E ...**equivalent**. Cor . Every parallelogram is**equivalent**to the rectangle which has the same base and the same altitude ... Page 59

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**equivalent**. PROPOSITION III . THEOREM . Two rectangles of the same altitude , are to each other as their bases . Let ABCD , AEFD be two rec- D tangles which have the common al- titude AD ; they are to each other as their bases AB , AE ... Page 61

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**equivalent**to the rec- tangle ABEF ( Prop . I. , Cor . ) . But the rectangle ABEF is measured by AB × AF ( Prop . IV ...**Equivalent**triangles , whose bases are equal , have equal altitudes ; and**equivalent**triangles , whose altitudes are ... Page 62

Elias Loomis. equal altitudes ; and

Elias Loomis. equal altitudes ; and

**equivalent**triangles , whose altitudes are equal , have equal bases . PROPOSITION ...**equivalent**to the parallelogram AGHD , and is measured by the product of AG by DE . Also , because AG is equal to DH ...### Other editions - View all

ELEMENTS OF GEOMETRY & CONIC S Elias 1811-1889 Loomis,Making of America Project No preview available - 2016 |

### Common terms and phrases

75 cents ABCD AC is equal allel altitude angle ABC angle ACB angle BAC Anthon's base BCDEF bisected chord circle circumference cone contained convex surface curve described diameter dicular draw drawn ellipse equal angles equal to AC equally distant equiangular equivalent exterior angle foci four right angles frustum greater Hence Prop hyperbola inscribed intersection join latus rectum Let ABC lines AC major axis mean proportional measured by half meet Muslin number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment Sheep extra side AC similar slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices

### Popular passages

Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.

Page 27 - VIf two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the...

Page 11 - A rhombus, is that which has all its sides equal, but its angles are not right angles.

Page 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.

Page 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.

Page 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Page 15 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.

Page 17 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.

Page 148 - I.), that every section of a sphere made by a plane is a circle.