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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 22.
Σελίδα 99
... semicircle , find a point C in AB such that , joining C to a fixed point D in the circumference , and erecting a perpendicular CE meeting the circumference in E , CE2CD2 may be equal to a given square . 6. If the square of a line CD ...
... semicircle , find a point C in AB such that , joining C to a fixed point D in the circumference , and erecting a perpendicular CE meeting the circumference in E , CE2CD2 may be equal to a given square . 6. If the square of a line CD ...
Σελίδα 101
... semi- circle AGE ; produce CB to meet it in G. The square described on BG will be equal to X. Dem . - Join FG . Then ... semicircle on the diameter is equal to the rectangle contained by the segments of the diameter . Exercises . 1 ...
... semi- circle AGE ; produce CB to meet it in G. The square described on BG will be equal to X. Dem . - Join FG . Then ... semicircle on the diameter is equal to the rectangle contained by the segments of the diameter . Exercises . 1 ...
Σελίδα 104
... semicircle , and CD any parallel chord , then CP2 + PD2 = AP2 + PB2 . 8. If A , B , C , D be four collinear points taken in order , AB . CD + BC . AD AC . BD . = 9. Three times the sum of the squares on the sides of any pentagon exceeds ...
... semicircle , and CD any parallel chord , then CP2 + PD2 = AP2 + PB2 . 8. If A , B , C , D be four collinear points taken in order , AB . CD + BC . AD AC . BD . = 9. Three times the sum of the squares on the sides of any pentagon exceeds ...
Σελίδα 130
... . Cor . - If AOB be a straight line , ACB will be a right angle — that is , the angle in a semicircle is a right angle ( compare XXXI . ) . PROP . XXI . - THEOREM . The angles ( 130 [ BOOK III . THE ELEMENTS OF EUCLID .
... . Cor . - If AOB be a straight line , ACB will be a right angle — that is , the angle in a semicircle is a right angle ( compare XXXI . ) . PROP . XXI . - THEOREM . The angles ( 130 [ BOOK III . THE ELEMENTS OF EUCLID .
Σελίδα 131
... semicircle , without using angles greater than two right angles : - A Let O be the centre . Join CO , and produce it to meet the circle again in E. Join DE . Now since O is the centre , the segment ACE is greater than a semicircle ...
... semicircle , without using angles greater than two right angles : - A Let O be the centre . Join CO , and produce it to meet the circle again in E. Join DE . Now since O is the centre , the segment ACE is greater than a semicircle ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 299 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Σελίδα 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...
Σελίδα 9 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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,