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 TrigonometryW. E. Dean, 1835 - 316 σελίδες |
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Αποτελέσματα 1 - 5 από τα 26.
Σελίδα 4
... coincide " in part , without coinciding altogether . " 4. A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the intersections of one superficies with another are also ...
... coincide " in part , without coinciding altogether . " 4. A superficies is that which has only length and breadth . " COR . The extremities of a superficies are lines ; and the intersections of one superficies with another are also ...
Σελίδα 7
... coincide in all their points of this kind are two circles , which have equal radii ; two triangles , which have all their sides equal respectively , & c . POSTULATES . 1. LET it be granted that a straight line may be drawn from any one ...
... coincide in all their points of this kind are two circles , which have equal radii ; two triangles , which have all their sides equal respectively , & c . POSTULATES . 1. LET it be granted that a straight line may be drawn from any one ...
Σελίδα 8
... coincide throughout their whole extent . They then fill the same space . 9. The whole is greater than any of its parts . 10. The whole is equal to the sum of all its parts . 11. All right angles are equal to one another . 12. " Two ...
... coincide throughout their whole extent . They then fill the same space . 9. The whole is greater than any of its parts . 10. The whole is equal to the sum of all its parts . 11. All right angles are equal to one another . 12. " Two ...
Σελίδα 9
... coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor . def . 3. ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces ...
... coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor . def . 3. ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces ...
Σελίδα 20
... coinciding with one another , which is impossible ( 11. Ax . ) A K C E Ꮐ I -B D H F The angles AGH , GHD therefore are not unequal , that is , they are equal to one another . Now , the angle EGB is equal to AGH ( S. 1. ) ; and AGH is ...
... coinciding with one another , which is impossible ( 11. Ax . ) A K C E Ꮐ I -B D H F The angles AGH , GHD therefore are not unequal , that is , they are equal to one another . Now , the angle EGB is equal to AGH ( S. 1. ) ; and AGH is ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal arc AC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw Prob 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 Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular plane polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 46 - 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.
Σελίδα 39 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 47 - 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 on the line between the points of section, is equal to the square on half the line.
Σελίδα 25 - 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.
Σελίδα 5 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 75 - 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.
Σελίδα 95 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 294 - 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.
Σελίδα 52 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Σελίδα 134 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.