Elements of Geometry: Plane and SolidAmerican Book Company, 1895 - 374 σελίδες |
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Σελίδα 12
... hence a point has no dimension , but only position . Just as we conceive a geometrical solid apart from mate- rial , so we may conceive of surfaces apart from solids , of lines apart from surfaces , and of points apart from lines ...
... hence a point has no dimension , but only position . Just as we conceive a geometrical solid apart from mate- rial , so we may conceive of surfaces apart from solids , of lines apart from surfaces , and of points apart from lines ...
Σελίδα 29
... Hence it is necessary to define the term equal in regard to figures in general . 61. Equal figures are such as can be made to coincide exactly ; that is , are equal in every respect . 62. THEOREM . Two triangles are equal if their ...
... Hence it is necessary to define the term equal in regard to figures in general . 61. Equal figures are such as can be made to coincide exactly ; that is , are equal in every respect . 62. THEOREM . Two triangles are equal if their ...
Σελίδα 43
... Hence , since BC can neither be equal to nor less than AC , it must be greater than 4C . Q.E.D. EXERCISE 47. Draw the diagram for Prop . XVII . , when the exterior angle ACD is acute . 48. Prove that a perpendicular from a vertex to the ...
... Hence , since BC can neither be equal to nor less than AC , it must be greater than 4C . Q.E.D. EXERCISE 47. Draw the diagram for Prop . XVII . , when the exterior angle ACD is acute . 48. Prove that a perpendicular from a vertex to the ...
Σελίδα 45
... , since then BC would be equal to B'C ' ( 66 ) ; nor can A be less than A ' , since then BC would be less than B'C ' ( 90 ) . Hence A must be greater than 4 ' . PERPENDICULARS . PROPOSITION XXI . PROBLEM . 92. To draw TRIANGLES . 45.
... , since then BC would be equal to B'C ' ( 66 ) ; nor can A be less than A ' , since then BC would be less than B'C ' ( 90 ) . Hence A must be greater than 4 ' . PERPENDICULARS . PROPOSITION XXI . PROBLEM . 92. To draw TRIANGLES . 45.
Σελίδα 46
... hence PA < PB ( 86 ) . ( 21 ) ( Const . ) ( 75 ) Q.E.F. B A M N * That is , the given line may be produced to any extent , if necessary . 94. DEFINITION . The distance of a point from a 46 - PLANE GEOMETRY . — BOOK I.
... hence PA < PB ( 86 ) . ( 21 ) ( Const . ) ( 75 ) Q.E.F. B A M N * That is , the given line may be produced to any extent , if necessary . 94. DEFINITION . The distance of a point from a 46 - PLANE GEOMETRY . — BOOK I.
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² altitude angle formed apothem arc AC bisector bisects chord circumf circumference circumscribed coincide cone of revolution Const construct cylinder DEFINITION diagonals diagram for Prop diameter dihedral angles divided draw edges equiangular equiangular polygon equidistant equilateral triangle equivalent EXERCISE find a point frustum given circle given line given point given straight line greater homologous hypotenuse inscribed intercept interior angles intersecting isosceles triangle line drawn line joining locus meet mid point number of sides numerical measures parallel parallelogram parallelopiped pass perimeter perpendicular plane MN polyhedral angle polyhedron prism produced PROPOSITION Prove pyramid quadrilateral radii radius ratio rect rectangle regular polygon regular polyhedrons right angle right triangle SCHOLIUM secant segment similar slant height sphere spherical polygon spherical triangle square straight angle tangent THEOREM triangle ABC trihedral vertex vertical angle volume
Δημοφιλή αποσπάσματα
Σελίδα 308 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Σελίδα 298 - Sphere is a body bounded by a uniformly curved surface, all the points of which are equally distant from a point within called the center.
Σελίδα 283 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Σελίδα 113 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Σελίδα 373 - The object of these primers is to convey information in such a manner as to make it both intelligible and interesting to very young pupils, and so to discipline their minds as to incline them to more systematic after-studies. They are not only an aid to the pupil, but to the teacher, lightening the task of each by an agreeable, easy, and natural method of instruction.
Σελίδα 178 - ... the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.
Σελίδα 123 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 118 - If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.
Σελίδα 179 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle.
Σελίδα 272 - 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.