The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
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Página 12
... Theorem is the formal statement of a property that may be demonstrated from known propositions . These propositions may themselves be theorems or axioms . A theorem consists of two parts , the hypothesis , or that which is assumed , and ...
... Theorem is the formal statement of a property that may be demonstrated from known propositions . These propositions may themselves be theorems or axioms . A theorem consists of two parts , the hypothesis , or that which is assumed , and ...
Página 13
... theorem ( IV . ) is called the obverse of ( 1. ) , and ( I. ) the obverse of ( II . ) . A Problem is a proposition in which something is proposed to be done , such as a line to be drawn , or a figure to be constructed , under some given ...
... theorem ( IV . ) is called the obverse of ( 1. ) , and ( I. ) the obverse of ( II . ) . A Problem is a proposition in which something is proposed to be done , such as a line to be drawn , or a figure to be constructed , under some given ...
Página 21
... THEOREM . If two angles ( B , C ) of a triangle be equal , the sides ( AC , AB ) opposite to them are also equal . A D Dem . - If AB , AC are not equal , one must be greater than the other . Suppose AB is the greater , and that the part ...
... THEOREM . If two angles ( B , C ) of a triangle be equal , the sides ( AC , AB ) opposite to them are also equal . A D Dem . - If AB , AC are not equal , one must be greater than the other . Suppose AB is the greater , and that the part ...
Página 30
... THEOREM . B D If two right lines ( AB , CD ) intersect one another , the opposite angles are equal ( CEA DEB , and ... theorem ? Ans . No theorem , only the axioms . 3. If two lines intersect , how many pairs of supplemental angles do ...
... THEOREM . B D If two right lines ( AB , CD ) intersect one another , the opposite angles are equal ( CEA DEB , and ... theorem ? Ans . No theorem , only the axioms . 3. If two lines intersect , how many pairs of supplemental angles do ...
Página 32
... THEOREM . Any two angles ( B , C ) of a triangle ( ABC ) are together less than two right angles . A Dem . - Produce BC to D ; then the exterior angle ACD is greater than ABC [ xvI . ] : to each add the angle ACB , and we have the sum ...
... THEOREM . Any two angles ( B , C ) of a triangle ( ABC ) are together less than two right angles . A Dem . - Produce BC to D ; then the exterior angle ACD is greater than ABC [ xvI . ] : to each add the angle ACB , and we have the sum ...
Términos y frases comunes
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
Pasajes populares
Página 295 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Página 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...
Página 9 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.