The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
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Σελίδα vii
... ratio of incommensurable quantities , the first twenty - one propositions of Book XI . , and an Appendix on the properties of the Prism , Pyra- mids , Cylinder , Sphere , and Cone . The present Edition has been very carefully read ...
... ratio of incommensurable quantities , the first twenty - one propositions of Book XI . , and an Appendix on the properties of the Prism , Pyra- mids , Cylinder , Sphere , and Cone . The present Edition has been very carefully read ...
Σελίδα 72
... ratio of 2 : 1 . 6. Construct a triangle , being given two sides and the median of the third side . 7. In every triangle the sum of the medians is less than the perimeter , and greater than three - fourths of the perimeter . 8 ...
... ratio of 2 : 1 . 6. Construct a triangle , being given two sides and the median of the third side . 7. In every triangle the sum of the medians is less than the perimeter , and greater than three - fourths of the perimeter . 8 ...
Σελίδα 96
... ratio . " Cor . 1. - The line CF is divided in " extreme and mean ratio " at A. Cor . 2. - If from the greater segment CA of CF we take a segment equal to AF , it is evident that CA will be divided into parts respectively equal to AH ...
... ratio . " Cor . 1. - The line CF is divided in " extreme and mean ratio " at A. Cor . 2. - If from the greater segment CA of CF we take a segment equal to AF , it is evident that CA will be divided into parts respectively equal to AH ...
Σελίδα 97
... ratio " are incommen- surable . Exercises . 1. Cut a line externally in " extreme and mean ratio . " 2. The difference between the squares on the segments of a line divided in " extreme and mean ratio " is equal to their rectangle . 3 ...
... ratio " are incommen- surable . Exercises . 1. Cut a line externally in " extreme and mean ratio . " 2. The difference between the squares on the segments of a line divided in " extreme and mean ratio " is equal to their rectangle . 3 ...
Σελίδα 99
... ratio " at B. PROP . XIII . - THEOREM . In any triangle ( ABC ) , the square on any side subtend- ing an acute angle ( C ) is less than the sum of the squares on the sides containing that angle , by twice the rectangle ( BC , CD ) ...
... ratio " at B. PROP . XIII . - THEOREM . In any triangle ( ABC ) , the square on any side subtend- ing an acute angle ( C ) is less than the sum of the squares on the sides containing that angle , by twice the rectangle ( BC , CD ) ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 295 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Σελίδα 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...
Σελίδα 9 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
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 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.
Σελίδα 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.