The Elements of Plane and Solid GeometryLongmans, Green, and, Company, 1871 - 285 sider |
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Side vi
... Proposition of Book I. may be instanced . The demonstration of this proposition would have been in no degree lengthened if Euclid had extended it to the equality of the triangles in all respects . As it is , he has restricted himself to ...
... Proposition of Book I. may be instanced . The demonstration of this proposition would have been in no degree lengthened if Euclid had extended it to the equality of the triangles in all respects . As it is , he has restricted himself to ...
Side vi
... Proposition of Book I. may be instanced . The demonstration of this proposition would have been in no degree lengthened if Euclid had extended it to the equality of the triangles in all respects . As it is , he has restricted himself to ...
... Proposition of Book I. may be instanced . The demonstration of this proposition would have been in no degree lengthened if Euclid had extended it to the equality of the triangles in all respects . As it is , he has restricted himself to ...
Side viii
... Proposition 4 of Book I. there is no sug- gestion of the possibility of the two triangles being so situated as to make it necessary for the plane of one of them to be reversed before superposition can take place ; the proof adopted ...
... Proposition 4 of Book I. there is no sug- gestion of the possibility of the two triangles being so situated as to make it necessary for the plane of one of them to be reversed before superposition can take place ; the proof adopted ...
Side ix
... proposition is essential to all that follow . Hence , an inevitable confusion arises in the mind of the reader between that which is possible theoretically and con- ceivably , and that which is possible in relation to the instruments to ...
... proposition is essential to all that follow . Hence , an inevitable confusion arises in the mind of the reader between that which is possible theoretically and con- ceivably , and that which is possible in relation to the instruments to ...
Side x
... Proposition 12 with Book III . Proposition 2 ) ; and in Book XI . recourse is neces- sarily had to hypothetical constructions , where lines are supposed to be drawn in space , concerning which all that is known is the possibility of the ...
... Proposition 12 with Book III . Proposition 2 ) ; and in Book XI . recourse is neces- sarily had to hypothetical constructions , where lines are supposed to be drawn in space , concerning which all that is known is the possibility of the ...
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Vanlige uttrykk og setninger
ABCD adjacent angle BAC applied base bisects called centre chords circumference coincide construction containing Corollary corresponding DEFINITION denominator described diameter difference dihedral angle distance divided double draw drawn equal EXAMPLES exterior angle extremities figure follows four given circle given plane given point given ratio given straight line greater half homologous inscribed inter intersection join length less Let ABC line joining locus magnitudes meet middle point multiple opposite sides pair parallel parallelogram passing perpendicular plane polygon portion position possible PROBLEM produced Prop proportional PROPOSITION Prove radius ratio rectangle regular remaining respectively respectively equal right angles segments sides similar Similarly situated square Take taken tangent third touching triangle ABC triangle DEF
Populære avsnitt
Side 15 - If two triangles have two sides of the one equal to two sides of the...
Side 101 - Through a given point to draw a straight line parallel to a given straight line. Let A be the given point, and BC the given straight line, it is required to draw a straight line through the point A, parallel to the line BC.
Side 126 - 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 222 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Side 188 - If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base ; the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Side 204 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Side 14 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Side 12 - 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 161 - Ir there be any number of magnitudes, and as many others, which, taken two and two in order, have the same ratio ; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words