Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement ... to which are Added, Elements of Plane and Sphericale Trigonometry ... From the Last London Ed., Enl |
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Page 195
... prism is a solid figure contained by plane figures , of which two thas are opposite are equal , similar , and parallel to one another ; and the others are parallelograms . 5. A parallelopiped is a solid figure contained by six ...
... prism is a solid figure contained by plane figures , of which two thas are opposite are equal , similar , and parallel to one another ; and the others are parallelograms . 5. A parallelopiped is a solid figure contained by six ...
Page 199
... prism CAE is equal to the prism CBE ( 1. 3. Sup . ) , and the solid AB is cut into two equal prisms by the plane CDEF . N. B. The insisting straight lines of a parallelopiped , mentioned in the following propositions , are the sides of ...
... prism CAE is equal to the prism CBE ( 1. 3. Sup . ) , and the solid AB is cut into two equal prisms by the plane CDEF . N. B. The insisting straight lines of a parallelopiped , mentioned in the following propositions , are the sides of ...
Page 200
... prisms DAG , HLN are equal ( 1. 3. Sup . ) . If therefore the prism LNH be taken from the solid , of which the base is the parallelogram AB , and FDKN the plane opposite to the base ; and if from this same solid there be taken the prism ...
... prisms DAG , HLN are equal ( 1. 3. Sup . ) . If therefore the prism LNH be taken from the solid , of which the base is the parallelogram AB , and FDKN the plane opposite to the base ; and if from this same solid there be taken the prism ...
Page 203
... prism and a parallelopiped , which have the same alti tude , are to one another as their bases ; that is , the prism BNM is to the parallelopiped CD as the triangle AEM to the parallelogram LG . For by the last Cor . the prism BNM is to the ...
... prism and a parallelopiped , which have the same alti tude , are to one another as their bases ; that is , the prism BNM is to the parallelopiped CD as the triangle AEM to the parallelogram LG . For by the last Cor . the prism BNM is to the ...
Page 205
... prisms are to one another in the ratio compounded of the ratios of their bases , and of their altitudes . For every prism is equal to a parallelopiped of the same altitude with it , and of an equal base ( 2. Cor . 8. 3. Sup . ) . PROP ...
... prisms are to one another in the ratio compounded of the ratios of their bases , and of their altitudes . For every prism is equal to a parallelopiped of the same altitude with it , and of an equal base ( 2. Cor . 8. 3. Sup . ) . PROP ...
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Common terms and phrases
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference coincide cosine cylinder definition demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB produced PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
Popular passages
Page 3 - 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 122 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 74 - The angle in a semicircle is a right angle: the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 44 - 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 5 - Let it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Page 290 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 277 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Page 143 - ... cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Page 7 - If two triangles have two sides of the one equal to two sides of the...
Page 26 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. Let AB, CD be equal and parallel straight lines, and joined towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel.