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 TrigonometryJ.P. Lippincott & Company, 1855 - 318 páginas |
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Página 195
... solid figure contained by plane figures , of which two that 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 quadrilateral ...
... solid figure contained by plane figures , of which two that 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 quadrilateral ...
Página 197
... solid KQ coincide with the other planes of the solid AG , each with each : wherefore the solids KQ and AG do wholly ... parallelopiped be cut by a plane parallel to two of its opposite planes , it will be divided into two solids , which will ...
... solid KQ coincide with the other planes of the solid AG , each with each : wherefore the solids KQ and AG do wholly ... parallelopiped be cut by a plane parallel to two of its opposite planes , it will be divided into two solids , which will ...
Página 198
... solid LP , are equal and similar to three planes of the solid KR , as also to three planes of the solid AV but the three planes opposite to these three are equal and similar to them ( 2 ... solid parallelopiped 198 SUPPLEMENT TO THE ELEMENTS.
... solid LP , are equal and similar to three planes of the solid KR , as also to three planes of the solid AV but the three planes opposite to these three are equal and similar to them ( 2 ... solid parallelopiped 198 SUPPLEMENT TO THE ELEMENTS.
Página 199
... solid parallelopiped be cut by a plane passing through the diagonals of two of the opposite planes , it will be cut into two equal prisms . Let AB be a solid parallelopiped , and DE , CF the diagonals of the op- posite parallelograms AH ...
... solid parallelopiped be cut by a plane passing through the diagonals of two of the opposite planes , it will be cut into two equal prisms . Let AB be a solid parallelopiped , and DE , CF the diagonals of the op- posite parallelograms AH ...
Página 200
... solid there be taken the prism AGD , the remaining solid , viz . the parallelopiped AH is equal to the remaining parallelopiped AK . PROP . VI . THEOR . Solid parallelopipeds upon the same base , and of the same altitude , the in ...
... solid there be taken the prism AGD , the remaining solid , viz . the parallelopiped AH is equal to the remaining parallelopiped AK . PROP . VI . THEOR . Solid parallelopipeds upon the same base , and of the same altitude , the in ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference 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 rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 51 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Página 29 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Página 12 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line.
Página 11 - 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.
Página 72 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.
Página 84 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 80 - 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.
Página 22 - Any two sides of a triangle are together greater than the third side.
Página 53 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Página 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.