The Elements of Plane and Solid GeometryLongmans, Green, and, Company, 1871 - 285 σελίδες |
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Σελίδα ix
... problems ; but this advantage is counterbalanced by the dis- advantage attending Euclid's treatment . The strictly logical form adopted by him induces , and was in- tended to induce , the belief that each individual proposition is ...
... problems ; but this advantage is counterbalanced by the dis- advantage attending Euclid's treatment . The strictly logical form adopted by him induces , and was in- tended to induce , the belief that each individual proposition is ...
Σελίδα x
... problems of squaring a circle , bisecting a cube , and trisecting an angle . Nor is this confusion . of ideas the only evil result arising from the exclusion of hypothetical constructions , for the treatise is thereby rendered ...
... problems of squaring a circle , bisecting a cube , and trisecting an angle . Nor is this confusion . of ideas the only evil result arising from the exclusion of hypothetical constructions , for the treatise is thereby rendered ...
Σελίδα xvii
... 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.
... 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.
Σελίδα xviii
... PROBLEMS OF 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 ...
... PROBLEMS OF 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 ...
Σελίδα 95
... the length of each chord be indefinitely diminished , the ultimate sum of the lengths of these chords is the length of the curved line . BOOK III . PROBLEMS OF CONSTRUCTION CONNECTED WITH THE STRAIGHT The Lengths of Curved Lines . 95.
... the length of each chord be indefinitely diminished , the ultimate sum of the lengths of these chords is the length of the curved line . BOOK III . PROBLEMS OF CONSTRUCTION CONNECTED WITH THE STRAIGHT The Lengths of Curved Lines . 95.
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 15 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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
Σελίδα 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...
Σελίδα 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'.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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