The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
Inni boken
Resultat 1-5 av 29
Side 22
... pair of conterminous sides ( AC , AD ) equal to one another , the other pair of conterminous sides ( BC , BD ) must be unequal . Dem . - 1 . Let the vertex of each triangle be without the other . Join CD . Then because AD is equal to AC ...
... pair of conterminous sides ( AC , AD ) equal to one another , the other pair of conterminous sides ( BC , BD ) must be unequal . Dem . - 1 . Let the vertex of each triangle be without the other . Join CD . Then because AD is equal to AC ...
Side 30
... proof of Prop . xшi . ? 2. What theorem ? Ans . No theorem , only the axioms . 3. If two lines intersect , how many pairs of supplemental angles do they make ? 4. What relation does Prop . XIV . bear to 30 [ BOOK I. THE ELEMENTS OF EUCLID .
... proof of Prop . xшi . ? 2. What theorem ? Ans . No theorem , only the axioms . 3. If two lines intersect , how many pairs of supplemental angles do they make ? 4. What relation does Prop . XIV . bear to 30 [ BOOK I. THE ELEMENTS OF EUCLID .
Side 44
... pair of lines which bisect the angles made by the fixed lines . 4. In a given right line find a point such that the ... pairs of whose opposite sides are parallel . DEF . III . - The right line joining either 44 [ BOOK I. THE ELEMENTS OF ...
... pair of lines which bisect the angles made by the fixed lines . 4. In a given right line find a point such that the ... pairs of whose opposite sides are parallel . DEF . III . - The right line joining either 44 [ BOOK I. THE ELEMENTS OF ...
Side 45
... pairs of opposite sides of a quadri- lateral be produced to meet , the right line joining their points of intersection is called its third diagonal . DEF . v . - A quadrilateral which has one pair of op- posite sides parallel is called ...
... pairs of opposite sides of a quadri- lateral be produced to meet , the right line joining their points of intersection is called its third diagonal . DEF . v . - A quadrilateral which has one pair of op- posite sides parallel is called ...
Side 50
... pair is equal to 2 ( n - 4 ) right angles . 4. If the line which bisects the external vertical angle be parallel to the base , the triangle is isosceles . 5. If two right - angled As ABC , ABD be on the same hypote- nuse AB , and the ...
... pair is equal to 2 ( n - 4 ) right angles . 4. If the line which bisects the external vertical angle be parallel to the base , the triangle is isosceles . 5. If two right - angled As ABC , ABD be on the same hypote- nuse AB , and the ...
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.