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 páginas |
Dentro del libro
Resultados 1-5 de 83
Página 9
... CIRCLE . XXXII . A circle is a plane figure formed by a curved line called the circumference , and is such that all right lines drawn from a certain point within the figure to the circumference are A equal to one another . is called the ...
... CIRCLE . XXXII . A circle is a plane figure formed by a curved line called the circumference , and is such that all right lines drawn from a certain point within the figure to the circumference are A equal to one another . is called the ...
Página 14
... circle BCD ( Post . I. ) . With B as centre , and BA as radius , describe the circle ACE , cutting the former circle in C. Join CA , CB ( Post . 1. ) . Then ABC is the equilateral D triangle required . Dem . - Because A is the centre of ...
... circle BCD ( Post . I. ) . With B as centre , and BA as radius , describe the circle ACE , cutting the former circle in C. Join CA , CB ( Post . 1. ) . Then ABC is the equilateral D triangle required . Dem . - Because A is the centre of ...
Página 15
... circle in the space ACB , bounded by the line AB and the two circles . PROP . II . - PROBLEM . From a given point ... circle ECH ( Post . III . ) . Produce DB to meet the circle ECH in E ( Post . II . ) . With D as centre , and DE as ...
... circle in the space ACB , bounded by the line AB and the two circles . PROP . II . - PROBLEM . From a given point ... circle ECH ( Post . III . ) . Produce DB to meet the circle ECH in E ( Post . II . ) . With D as centre , and DE as ...
Página 16
... circles . If he allowed the mechanical use of the rule and compass he could give methods of solving many problems that go beyond the limits of the " geometry of the point , line , and circle . " - See Notes D , F at the end of this work ...
... circles . If he allowed the mechanical use of the rule and compass he could give methods of solving many problems that go beyond the limits of the " geometry of the point , line , and circle . " - See Notes D , F at the end of this work ...
Página 37
... circle KDL ( Post . III . ) ; and with G as centre , and GH as radius , describe the circle KHL , intersecting the former circle in K. Join KF , KG . KFG is the triangle required . Dem . - Since F is the centre of the circle KDL , FK is ...
... circle KDL ( Post . III . ) ; and with G as centre , and GH as radius , describe the circle KHL , intersecting the former circle in K. Join KF , KG . KFG is the triangle required . Dem . - Since F is the centre of the circle KDL , FK is ...
Otras ediciones - Ver todas
Términos y frases comunes
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
Pasajes populares
Página 299 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Página 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...
Página 9 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 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.
Página 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...
Página 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.
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 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.
Página 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,