The First Six Books of the Elements of Euclid: And Propositions I-XXI of Book XI, and an Appendix on the Cylinder, Sphere, Cone, Etc., with Copious Annotations and Numerous ExercisesHodges, Figgis, & Company, 1885 - 312 sider |
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Side 17
... respectively to two sides ( ED , DF ) of the other , and have also the angles ( A , D ) included by those sides equal , the triangles shall be equal in every respect- that is , their bases or third sides ( BC , EF ) shall be equal , and ...
... respectively to two sides ( ED , DF ) of the other , and have also the angles ( A , D ) included by those sides equal , the triangles shall be equal in every respect- that is , their bases or third sides ( BC , EF ) shall be equal , and ...
Side 19
... respectively equal to the sides GA , AB in the other ; and the included angle A is common to both triangles . Hence [ Iv . ] the base FC is equal to GB , the angle AFC is equal to AGB , and the angle ACF is equal to the angle ABG ...
... respectively equal to the sides GA , AB in the other ; and the included angle A is common to both triangles . Hence [ Iv . ] the base FC is equal to GB , the angle AFC is equal to AGB , and the angle ACF is equal to the angle ABG ...
Side 20
... BA , AC of one respectively equal to the sides AC , AD of the other , and the included angles equal ; therefore [ Iv . ] the angle ACB oppo- B C 1 site to the side AB is equal to the 20 [ BOOK I. THE ELEMENTS OF EUCLID .
... BA , AC of one respectively equal to the sides AC , AD of the other , and the included angles equal ; therefore [ Iv . ] the angle ACB oppo- B C 1 site to the side AB is equal to the 20 [ BOOK I. THE ELEMENTS OF EUCLID .
Side 23
... respectively equal to two sides ( DE , DF ) of the other , and have also the base ( BC ) of one equal to the base ( EF ) of the other ; then the two triangles shall be equal , and the angles of one shall be respectively equal to the ...
... respectively equal to two sides ( DE , DF ) of the other , and have also the base ( BC ) of one equal to the base ( EF ) of the other ; then the two triangles shall be equal , and the angles of one shall be respectively equal to the ...
Side 25
... respectively equal to EA , AF , and the base DF is equal to the base EF , because they are the sides of an equi- lateral triangle ( Def . XXI . ) . Therefore [ VIII . ] the angle DAF is equal to the angle EAF ; hence the angle BAC is ...
... respectively equal to EA , AF , and the base DF is equal to the base EF , because they are the sides of an equi- lateral triangle ( Def . XXI . ) . Therefore [ VIII . ] the angle DAF is equal to the angle EAF ; hence the angle BAC is ...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ... Euclid,John Casey Uten tilgangsbegrensning - 1885 |
Vanlige uttrykk og setninger
ABCD AC is equal adjacent angles altitude angle ABC angle ACB angle BAC angular points Axiom bisector bisects centre chord circles touch circumference circumscribed circle collinear concurrent lines const coplanar cyclic quadrilateral Dem.-Let diagonals diameter divided draw equal angles equal to AC equiangular equilateral triangle escribed circles Euclid Exercises exterior angle Geometry given circle given line given point greater Hence the angle hypotenuse inscribed less line AC line joining locus manner meet middle points multiple nine-points circle opposite sides parallel parallelogram parallelopiped perpendicular plane points of intersection prism PROP Proposition prove radii radius rectangle contained rectilineal figure regular polygon respectively equal right angles right line segments semicircle sides AC similar square on AC tangent theorem triangle ABC vertex vertical angle
Populære avsnitt
Side 299 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Side 186 - When of the equimultiples of four magnitudes (taken as in the fifth definition) the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth...
Side 9 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 104 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Side 124 - The diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Side 230 - If from any angle of a triangle, a straight line be drawn perpendicular to the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.
Side 29 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 63 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 128 - The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair.
Side 22 - ACB, DB is equal to AC, and BC common to both ; the two sides DB, BC, are equal to the two AC, CB, each to each, and the angle DBC is equal to the angle ACB : therefore, the base DC is equal to the base AB, and the triangle DBC (Mr. Southey) is equal to the triangle ACB, the less to the greater, which is absurd,