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 sider |
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Resultat 1-5 av 60
Side xi
... proved . Indeed those who make the ob- jection just stated , do not seem to have reflected suffi- ciently on the end of Mathematical Demonstration , which is not only to prove the truth of a certain proposition , but to show its ...
... proved . Indeed those who make the ob- jection just stated , do not seem to have reflected suffi- ciently on the end of Mathematical Demonstration , which is not only to prove the truth of a certain proposition , but to show its ...
Side 18
... proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same are equal to one another , ( 1. Axiom ) ; therefore CA is equal to CB ; wherefore CA , AB , CB are equal to one ...
... proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB ; now things which are equal to the same are equal to one another , ( 1. Axiom ) ; therefore CA is equal to CB ; wherefore CA , AB , CB are equal to one ...
Side 20
... angle AGB : And because the whole AF is equal to the whole AG , and the part AB to the part AC : the remain- der BF shall be equal ( 3. Ax . ) to the F C B G D / E remainder CG ; and FC was proved to be equal 20 ELEMENTS.
... angle AGB : And because the whole AF is equal to the whole AG , and the part AB to the part AC : the remain- der BF shall be equal ( 3. Ax . ) to the F C B G D / E remainder CG ; and FC was proved to be equal 20 ELEMENTS.
Side 21
... proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3 : 1. ) , and their remaining angles ...
... proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3 : 1. ) , and their remaining angles ...
Side 22
... proved to be greater than the same BCD ; which is impossi- The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . ble . Therefore , upon the same base , and on the same side of it , there ...
... proved to be greater than the same BCD ; which is impossi- The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . ble . Therefore , upon the same base , and on the same side of it , there ...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Uten tilgangsbegrensning - 1826 |
Elements of Geometry: Containing the First Six Books of Euclid; With Two ... Formerly Chairman Department of Immunology John Playfair Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 41 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.