## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |

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Resultat 1-5 av 25

Side 115

The

of two opposite sides , taken as bases . And the

perpendicular drawn between its two parallel sides . A PROP . I. THEOR .

Triangles ...

The

**altitude**of a parallelogram is the perpendicular which measures the distanceof two opposite sides , taken as bases . And the

**altitude**of a trapezoid is theperpendicular drawn between its two parallel sides . A PROP . I. THEOR .

Triangles ...

Side 117

... the same

are to one another as their bases ; and for the same reason , as the triangle CDE

to the triangle ADE , so is CE to EA . Therefore , as BD to DĂ , so is CE to EA ( 11.

... the same

**altitude**, viz . the perpendicular drawn from the point E to AB , theyare to one another as their bases ; and for the same reason , as the triangle CDE

to the triangle ADE , so is CE to EA . Therefore , as BD to DĂ , so is CE to EA ( 11.

Side 126

... as GB С G to BF . Complete the parallelogram FE ; and because the

parallelograms AB , BC are equal , and FE is another parallelogram , AB : FE ::

BC : FE ( 7. 5. ) : but because the parallelograms AB , FE have the same

AB : FE ...

... as GB С G to BF . Complete the parallelogram FE ; and because the

parallelograms AB , BC are equal , and FE is another parallelogram , AB : FE ::

BC : FE ( 7. 5. ) : but because the parallelograms AB , FE have the same

**altitude**,AB : FE ...

Side 135

Hence , any two rectangles are to each other as the products of their bases

multiplied by their

understand by ...

Hence , any two rectangles are to each other as the products of their bases

multiplied by their

**altitudes**. SCHOLIUM . Hence the product of the base by the**altitude**may be assumed as the measure of a rectangle , provided weunderstand by ...

Side 136

Hence , the area of any parallelogram is equal to the product of its base by its

product of its base by half its

parallelograms ...

Hence , the area of any parallelogram is equal to the product of its base by its

**altitude**. Cor . 2. It likewise follows , that the area of any triangle is equal to theproduct of its base by half its

**altitude**. PROP . XXIV . THEOR . Theparallelograms ...

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### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction cosine cylinder definition demonstrated described diameter difference distance divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremities fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism Prob produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides similar sine solid square straight line taken tangent THEOR third touch triangle ABC wherefore whole