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 σελίδες |
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Σελίδα 188
... prism is a 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 . V. A parallelepiped is a solid figure contained by six ...
... prism is a 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 . V. A parallelepiped is a solid figure contained by six ...
Σελίδα 192
... prisms . Let AB be a solid parallelopiped , and DE , CF the diagonals of the opposite parallelograms AH , GB , viz . those which are drawn betwixt the equal angles in each ; and because CD , FE are each of them pa- rallel to GA , though ...
... prisms . Let AB be a solid parallelopiped , and DE , CF the diagonals of the opposite parallelograms AH , GB , viz . those which are drawn betwixt the equal angles in each ; and because CD , FE are each of them pa- rallel to GA , though ...
Σελίδα 193
... 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 . Q. E. D. N. B. The insisting straight lines of a parallelopiped , mentioned in the following propositions , are the ...
... 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 . Q. E. D. N. B. The insisting straight lines of a parallelopiped , mentioned in the following propositions , are the ...
Σελίδα 194
... 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 ...
Σελίδα 197
... 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 DPG as the triangle AME to the triangle CGF , and therefore the prism BNM is to twice the prism DPG ...
... 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 DPG as the triangle AME to the triangle CGF , and therefore the prism BNM is to twice the prism DPG ...
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Elements of Geometry: Containing the First Six Books of Euclid; With Two ... Formerly Chairman Department of Immunology John Playfair Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.