The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
Inni boken
Resultat 1-5 av 61
Side 29
... segment . Cor . 3. - The bisector of any angle bisects the cor- responding re - entrant angle . Cor . 4. - The bisectors of two supplemental angles are at right angles to each other . Cor . 5. - The angle EBA is half the difference of ...
... segment . Cor . 3. - The bisector of any angle bisects the cor- responding re - entrant angle . Cor . 4. - The bisectors of two supplemental angles are at right angles to each other . Cor . 5. - The angle EBA is half the difference of ...
Side 69
... segments , the sum of the squares on one set of alternate segments is equal to the sum of the squares on the remaining set . 18. The sum of the squares on lines drawn from any point to one pair of opposite angles of a rectangle is equal ...
... segments , the sum of the squares on one set of alternate segments is equal to the sum of the squares on the remaining set . 18. The sum of the squares on lines drawn from any point to one pair of opposite angles of a rectangle is equal ...
Side 77
... segments , and C a point of division . A с B П. If C be taken in the line AB produced , AC , CB are still called the segments of the line AB ; but C is called a point of external division . A B с III . A parallelogram whose angles are ...
... segments , and C a point of division . A с B П. If C be taken in the line AB produced , AC , CB are still called the segments of the line AB ; but C is called a point of external division . A B с III . A parallelogram whose angles are ...
Side 79
... segments of a line divided in various ways . All these can be proved in the most simple manner by Algebraic Multiplication . We recommend the stu- dent to make himself acquainted with the proofs by this BOOK II . ] THE ELEMENTS OF ...
... segments of a line divided in various ways . All these can be proved in the most simple manner by Algebraic Multiplication . We recommend the stu- dent to make himself acquainted with the proofs by this BOOK II . ] THE ELEMENTS OF ...
Side 80
... segments ( AC , CB ) . A C B Dem . - On AB describe the square ABDF [ I. XLVI . ] , and through C draw CE parallel to AF [ I. XXXI . ] . Now , since AB is equal to AF , the rectangle con- tained by AB and AC is equal to the rectangle ...
... segments ( AC , CB ) . A C B Dem . - On AB describe the square ABDF [ I. XLVI . ] , and through C draw CE parallel to AF [ I. XXXI . ] . Now , since AB is equal to AF , the rectangle con- tained by AB and AC is equal to the rectangle ...
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.