Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 σελίδες |
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Σελίδα
... indebted for the invaluable aid he has kindly rendered me during the preparation of this work . WM . H. H. PHILLIPS . WILBRAHAM , MASS . , July 1 , 1874 . CONTENTS . PLANE GEOMETRY . GENERAL PRINCIPLES EXPLANATION OF SYMBOLS vi PREFACE .
... indebted for the invaluable aid he has kindly rendered me during the preparation of this work . WM . H. H. PHILLIPS . WILBRAHAM , MASS . , July 1 , 1874 . CONTENTS . PLANE GEOMETRY . GENERAL PRINCIPLES EXPLANATION OF SYMBOLS vi PREFACE .
Σελίδα
... 83 90 93 97 BOOK IV . REGULAR POLYGONS , AND THE CIRCLE 105 MEASUREMENT OF THE CIRCLE . 112 SOLID GEOMETRY . BOOK V. STRAIGHT LINES , AND PLANES Lines which cut a Plane 117 118 PAGE Lines parallel to a Plane 123 Planes which cut.
... 83 90 93 97 BOOK IV . REGULAR POLYGONS , AND THE CIRCLE 105 MEASUREMENT OF THE CIRCLE . 112 SOLID GEOMETRY . BOOK V. STRAIGHT LINES , AND PLANES Lines which cut a Plane 117 118 PAGE Lines parallel to a Plane 123 Planes which cut.
Σελίδα
... Plane 123 Planes which cut each other : Dihedral Angles 125 Parallel Planes 128 Polyhedral Angles 131 Symmetrical Polyhedrals 132 Polar Polyhedrals 132 BOOK VI . POLYHEDRONS 138 The Prism 139 Pyramids 141 Regular Polyhedrons . 143 BOOK ...
... Plane 123 Planes which cut each other : Dihedral Angles 125 Parallel Planes 128 Polyhedral Angles 131 Symmetrical Polyhedrals 132 Polar Polyhedrals 132 BOOK VI . POLYHEDRONS 138 The Prism 139 Pyramids 141 Regular Polyhedrons . 143 BOOK ...
Σελίδα 2
... plane when the straight line joining any two of its points lies wholly in the surface . 13. A curved surface is a surface which is neither a plane , nor composed of planes ; as the surface of a ball , pipe , & c . 14. A geometrical ...
... plane when the straight line joining any two of its points lies wholly in the surface . 13. A curved surface is a surface which is neither a plane , nor composed of planes ; as the surface of a ball , pipe , & c . 14. A geometrical ...
Σελίδα 4
... refer to books , and Arabic numerals to articles ; thus ( I. , 38 ) refers to Book I. , Article XXXVIII . ( 18 ) refers to Article XVIII . of the same book . PLANE GEOMETRY . BOOK I. LINES AND ANGLES . I. EXPLANATION OF SYMBOLS.
... refer to books , and Arabic numerals to articles ; thus ( I. , 38 ) refers to Book I. , Article XXXVIII . ( 18 ) refers to Article XVIII . of the same book . PLANE GEOMETRY . BOOK I. LINES AND ANGLES . I. EXPLANATION OF SYMBOLS.
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² adjacent angles altitude angles are equal anharmonic ratio bisect called centre chord circle circumference circumscribed polygon cone congruent construct cylinder diagonals diameter dihedrals distance divided draw equal altitudes equal bases equally distant equations equiangular EXERCISE exterior angle face angles formed frustum Geometry harmonically hence homologous HYPOTH infinite number inscribed angle intersection lateral edges line joining lines drawn locus middle point number of sides Olney's opposite sides P₁ parallel lines parallelogram parallelopiped pass perpendicular plane angle point of contact polar pole polyhedral polyhedron prism Problem PROOF proportional PROVED pyramid quadrilateral radical axis radii radius rectangle regular polygon right angles SCHOLIUM segments solid angle sphere spherical excess spherical polygon spherical triangle square straight line symmetrical tangent Theorem triangle ABC trihedrals vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 19 - IF two triangles have two sides of the one equal to two sides of the...
Σελίδα 34 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Σελίδα 14 - A Polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a pentagon; one of six sides, a hexagon; one of seven sides, a heptagon; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon, &c.
Σελίδα 75 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Σελίδα 170 - Two prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes; prisms having equal altitudes are to each other as their bases ; prisms having equivalent bases and equal altitudes are equivalent.
Σελίδα 69 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.