The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
Inni boken
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Side 37
... ABCD lie within a convex poly- gonal line AMND terminating in the same extremities , the length of the former is less than that of the latter . A B N PROP . XXII . - PROBLEM . To construct a triangle whose three sides shall be respec ...
... ABCD lie within a convex poly- gonal line AMND terminating in the same extremities , the length of the former is less than that of the latter . A B N PROP . XXII . - PROBLEM . To construct a triangle whose three sides shall be respec ...
Side 54
... ABCD is a parallelogram , AD is equal to BC [ XXXIV ] ; and since BCEF is a parallelogram , EF is equal to BC ; therefore ( see fig . ( a ) ) take away ED , and in fig . ( B ) add ED , and we have in each case AE equal to DF , and BA is ...
... ABCD is a parallelogram , AD is equal to BC [ XXXIV ] ; and since BCEF is a parallelogram , EF is equal to BC ; therefore ( see fig . ( a ) ) take away ED , and in fig . ( B ) add ED , and we have in each case AE equal to DF , and BA is ...
Side 55
... ABCD , EBCF can be divided into parts and rearranged so as to make it congruent with the other . This Proposition affords the first instance in the Elements in which equality which is not congruence occurs . This equality is expressed ...
... ABCD , EBCF can be divided into parts and rearranged so as to make it congruent with the other . This Proposition affords the first instance in the Elements in which equality which is not congruence occurs . This equality is expressed ...
Side 56
... ABCD , any right line be drawn cutting the sides AB , BC in the points E , F , and ED , FD be joined , the triangle EFD is less than half the parallelogram . PROP . XXXVIII . - THEOREM . Two triangles on 56 [ BOOK I. THE ELEMENTS OF ...
... ABCD , any right line be drawn cutting the sides AB , BC in the points E , F , and ED , FD be joined , the triangle EFD is less than half the parallelogram . PROP . XXXVIII . - THEOREM . Two triangles on 56 [ BOOK I. THE ELEMENTS OF ...
Side 60
... ABCD is double of the triangle ABC [ xxxiv . ] ; A but the triangle ABC is equal to the triangle EBC [ xxxvII . ] . Therefore the parallelogram ABCD is double of the triangle EBC . Cor . 1. - If a triangle and B C a parallelogram have ...
... ABCD is double of the triangle ABC [ xxxiv . ] ; A but the triangle ABC is equal to the triangle EBC [ xxxvII . ] . Therefore the parallelogram ABCD is double of the triangle EBC . Cor . 1. - If a triangle and B C a parallelogram have ...
Vanlige uttrykk og setninger
ABCD AC is equal AD² 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 isosceles 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 295 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Side 182 - 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 102 - 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 122 - 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 226 - 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 126 - 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 194 - If there be any number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.