The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
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Resultater 1-5 af 41
Side 19
... triangle and the opposite vertices of the equilateral triangles are equal . ( This Proposition should be proved after the student has read Prop . XXXII . ) PROP . V. - THEOREM . The angles ( ABC , ACB ) at the base ( BC ) of an isosceles ...
... triangle and the opposite vertices of the equilateral triangles are equal . ( This Proposition should be proved after the student has read Prop . XXXII . ) PROP . V. - THEOREM . The angles ( ABC , ACB ) at the base ( BC ) of an isosceles ...
Side 20
... angle FBC equal to the angle GCB , and these are the angles below the base . Also the angle FCB equal to GBC ; but the whole angle FCA has been proved equal to the whole angle GBA . Hence the remaining angle ACB is equal to the remaining ...
... angle FBC equal to the angle GCB , and these are the angles below the base . Also the angle FCB equal to GBC ; but the whole angle FCA has been proved equal to the whole angle GBA . Hence the remaining angle ACB is equal to the remaining ...
Side 21
Euclides John Casey. site to the side AB is equal to the angle ADC opposite to the side AC ; but the angle ADC is equal to ABC ; therefore ACB is equal to ABC . Cor . - Every equilateral triangle is equiangular . DEF . - A line in any ...
Euclides John Casey. site to the side AB is equal to the angle ADC opposite to the side AC ; but the angle ADC is equal to ABC ; therefore ACB is equal to ABC . Cor . - Every equilateral triangle is equiangular . DEF . - A line in any ...
Side 22
... ACB - the less to the greater , which is absurd ; hence AC , AB are not unequal , that is , they are equal ... angle ACD is equal to the angle ADC ; but ADC is greater than BDC ( Axiom IX . ) ; therefore ACD is greater than BDC much more ...
... ACB - the less to the greater , which is absurd ; hence AC , AB are not unequal , that is , they are equal ... angle ACD is equal to the angle ADC ; but ADC is greater than BDC ( Axiom IX . ) ; therefore ACD is greater than BDC much more ...
Side 26
... triangle ACB [ 1 ] Bisect the angle ACB by the line CD [ Ix . ] , meeting AB in D , then AB is bisected in D. Dem . The two triangles ACD , BCD , have the side AC equal to BC , being the sides of an equilateral triangle , and CD common ...
... triangle ACB [ 1 ] Bisect the angle ACB by the line CD [ Ix . ] , meeting AB in D , then AB is bisected in D. Dem . The two triangles ACD , BCD , have the side AC equal to BC , being the sides of an equilateral triangle , and CD common ...
Almindelige termer og sætninger
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 passager
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.