The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
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Página x
... , 253 Exercises , 255 BOOK XI . Theory of Planes , Coplanar Lines , and Solid Angles , 267 Definitions , • Propositions I. - XXI . , Exercises , 267 267 281 APPENDIX . Prism , Pyramid , Cylinder , Sphere , X CONTENTS .
... , 253 Exercises , 255 BOOK XI . Theory of Planes , Coplanar Lines , and Solid Angles , 267 Definitions , • Propositions I. - XXI . , Exercises , 267 267 281 APPENDIX . Prism , Pyramid , Cylinder , Sphere , X CONTENTS .
Página 1
... plane , and that department of Geometry which is occu- pied with the lines and curves drawn on a plane is called Plane Geometry ; that which demonstrates the properties of solids , of curved surfaces , and the figures described on ...
... plane , and that department of Geometry which is occu- pied with the lines and curves drawn on a plane is called Plane Geometry ; that which demonstrates the properties of solids , of curved surfaces , and the figures described on ...
Página 2
... plane are the right line and circle , and the study of the properties of the point , the right line , and the circle , is the introduction to Geometry , of which it forms an extensive and im- portant department . This is the part of ...
... plane are the right line and circle , and the study of the properties of the point , the right line , and the circle , is the introduction to Geometry , of which it forms an extensive and im- portant department . This is the part of ...
Página 5
... plane . A plane is perfectly flat and even , like the surface of still water , or of a smooth floor . - NEWCOMB . FIGURES . VII . Any combination of points , of lines , or of points and lines in a plane , is called a plane figure . If a ...
... plane . A plane is perfectly flat and even , like the surface of still water , or of a smooth floor . - NEWCOMB . FIGURES . VII . Any combination of points , of lines , or of points and lines in a plane , is called a plane figure . If a ...
Página 6
... plane of the angle , from the position of coincidence with one leg to that of coincidence with the other , is said to turn through the angle , and the angle is the greater as the quantity of turning is the greater . Again , since the ...
... plane of the angle , from the position of coincidence with one leg to that of coincidence with the other , is said to turn through the angle , and the angle is the greater as the quantity of turning is the greater . Again , since the ...
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.