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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Σελίδα 69
... triangle perpendicu- lars are let fall on the opposite sides ; prove that the sum of the rectangles contained by the sides and their lower segments is equal to the square on the base . PROP . XLVIII . - THEOREM . If the square on one ...
... triangle perpendicu- lars are let fall on the opposite sides ; prove that the sum of the rectangles contained by the sides and their lower segments is equal to the square on the base . PROP . XLVIII . - THEOREM . If the square on one ...
Σελίδα 76
... rectangular parallelograms , each contain- ing 12 square inches , the square foot contains 144 square inches . In the same manner it can be shown that a 76 [ BOOK II . THE ELEMENTS OF EUCLID . BOOK II Theory of Rectangles,
... rectangular parallelograms , each contain- ing 12 square inches , the square foot contains 144 square inches . In the same manner it can be shown that a 76 [ BOOK II . THE ELEMENTS OF EUCLID . BOOK II Theory of Rectangles,
Σελίδα 77
... contained by any two ad- jacent sides ; for if we multiply the length of one by the length of the other we have the area . Thus , if AB , AD be two adjacent sides of a rectangle ... rectangle . IV . A rectangle is said to D be contained by ...
... contained by any two ad- jacent sides ; for if we multiply the length of one by the length of the other we have the area . Thus , if AB , AD be two adjacent sides of a rectangle ... rectangle . IV . A rectangle is said to D be contained by ...
Σελίδα 78
... rectangle contained by the two lines ( A , BC ) , is equal to the sum of the rectangles contained by the undivided line ( A ) and the several parts of the divided line . F G H K Dem . - Erect BF at right angles to BC [ I. , XI . ] and ...
... rectangle contained by the two lines ( A , BC ) , is equal to the sum of the rectangles contained by the undivided line ( A ) and the several parts of the divided line . F G H K Dem . - Erect BF at right angles to BC [ I. , XI . ] and ...
Σελίδα 79
... contained by A and BC is BK . In like manner the rectangle contained by A and BD is BG . Again , since A is equal to BF ( const . ) , and BF is equal to DG [ I. xxxiv . ] , A is equal to DG . Hence the rectangle contained by A and DE is ...
... contained by A and BC is BK . In like manner the rectangle contained by A and BD is BG . Again , since A is equal to BF ( const . ) , and BF is equal to DG [ I. xxxiv . ] , A is equal to DG . Hence the rectangle contained by A and DE is ...
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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,