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 TrigonometryMarot & Walter, 1826 - 320 páginas |
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Página iii
... passing through the hands of the ancient editors , during the decline of science , had suffered some diminu- tion of their excellence , and much skill and learning have been employed by the modern mathematicians to deliver them from ...
... passing through the hands of the ancient editors , during the decline of science , had suffered some diminu- tion of their excellence , and much skill and learning have been employed by the modern mathematicians to deliver them from ...
Página 44
... passes , and let BK , KD be the other parallelograms , which make up the whole figure ABCD and are there- fore called the complements : The E complement BK is equal to the com- plement KD . Because ABCD is a parallelogram and AC its ...
... passes , and let BK , KD be the other parallelograms , which make up the whole figure ABCD and are there- fore called the complements : The E complement BK is equal to the com- plement KD . Because ABCD is a parallelogram and AC its ...
Página 63
... pass . through the centre , it will cut that line at right angles ; and if it cut it at right angles , it will bisect it . Let ABC be a circle , and let CD , a straight line drawn through the centre bisect any straight line AB , which ...
... pass . through the centre , it will cut that line at right angles ; and if it cut it at right angles , it will bisect it . Let ABC be a circle , and let CD , a straight line drawn through the centre bisect any straight line AB , which ...
Página 64
... pass through the centre , they do not bisect each other , Let ABCD be a circle , and AC , BD two straight lines in it , which cut one another in the point E , and do not both pass through the cen- tre : AC , BD do not bisect one another ...
... pass through the centre , they do not bisect each other , Let ABCD be a circle , and AC , BD two straight lines in it , which cut one another in the point E , and do not both pass through the cen- tre : AC , BD do not bisect one another ...
Página 65
... passing through the centre is always greater than one more remote from it : And from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line . Let ABCD be a ...
... passing through the centre is always greater than one more remote from it : And from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line . Let ABCD be a ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC meet multiple opposite angle parallel parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 125 - 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.
Página 39 - 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.
Página 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 19 - BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.
Página 145 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.
Página 30 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Página 136 - FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (6.
Página 51 - 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.
Página 20 - DEF, and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other and be equal to them, viz. the angle ABC to the angle DEF, and the angle ACB to DFE.
Página 55 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.