The Elements of Plane and Solid GeometryLongmans, Green, and, Company, 1871 - 285 sider |
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Side ix
... constructions . Euclid's Geometry comprises two classes of propo- sitions , entirely different in their aim and nature , but mixed up together without any indication of this difference . The propositions in the one class are theoretical ...
... constructions . Euclid's Geometry comprises two classes of propo- sitions , entirely different in their aim and nature , but mixed up together without any indication of this difference . The propositions in the one class are theoretical ...
Side x
... constructions , for the treatise is thereby rendered inconsistent with itself , and properties of the circle are assumed in Book I. which are demon- strated at full length in Book III . ( compare , for example , Book I. Proposition 12 ...
... constructions , for the treatise is thereby rendered inconsistent with itself , and properties of the circle are assumed in Book I. which are demon- strated at full length in Book III . ( compare , for example , Book I. Proposition 12 ...
Side xvii
... THE CONTACT OF STRAIGHT LINES AND CIRCLES WITH CIRCLES . IV . ON LOCI CONNECTED WITH THE CIRCLE 77 90 BOOK III . PROBLEMS OF CONSTRUCTION CONNECTED WITH THE STRAIGHT LINE AND CIRCLE . 96 BOOK IV . On Areas . SECTION I. THEOREMS PAGE.
... THE CONTACT OF STRAIGHT LINES AND CIRCLES WITH CIRCLES . IV . ON LOCI CONNECTED WITH THE CIRCLE 77 90 BOOK III . PROBLEMS OF CONSTRUCTION CONNECTED WITH THE STRAIGHT LINE AND CIRCLE . 96 BOOK IV . On Areas . SECTION I. THEOREMS PAGE.
Side xviii
... CONSTRUCTION CONNECTED WITH AREAS 136 BOOK V. I. ON RATIO AND PROPORTION . 143 II . ON THE COMMENSURABILITY AND INCOMMENSURABILITY OF MAGNITUDES OF LIKE KINDS 168 BOOK VI . Application of Proportion to Geometry . I. MISCELLANEOUS ...
... CONSTRUCTION CONNECTED WITH AREAS 136 BOOK V. I. ON RATIO AND PROPORTION . 143 II . ON THE COMMENSURABILITY AND INCOMMENSURABILITY OF MAGNITUDES OF LIKE KINDS 168 BOOK VI . Application of Proportion to Geometry . I. MISCELLANEOUS ...
Side 30
... construction ) , therefore the triangles AEB and CEF are equal in all their parts , therefore the angle ACF is equal to the angle BAC , therefore the angle ACD is greater than the angle BAC . If AC be produced to G , it may be 30 Geometry .
... construction ) , therefore the triangles AEB and CEF are equal in all their parts , therefore the angle ACF is equal to the angle BAC , therefore the angle ACD is greater than the angle BAC . If AC be produced to G , it may be 30 Geometry .
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Vanlige uttrykk og setninger
ABC and DEF ABCD adjacent angles angle ABC angle ACB angle BAC BC is equal centre circumference coincide common measure construction Corollary diameter dicular dihedral angle distance divided equal angles equal to AC equidistant exterior angle figure four right angles given angle given circle given plane given point given ratio given straight line greater homologous inscribed intersecting straight lines length less Let ABC line of intersection locus magnitudes meet the circle middle point multiple number of sides opposite sides parallelogram pentagon perpen perpendicular plane AC point F produced Prop PROPOSITION PROPOSITION 13 Prove radii radius rectangle regular polygon respectively equal rhombus right angles segments side BC similar triangles Similarly situated square straight line AB straight line BC subtended tangent 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