Plane and Solid GeometryLongmans, Green and Company, 1898 - 210 σελίδες |
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Σελίδα vi
... problems . Ordinarily the problem is presumed to be solved , and then a demonstra- tion is given to show that the solution was correct . This does not appear to me to be in the line of discovery . I have in all cases started with a ...
... problems . Ordinarily the problem is presumed to be solved , and then a demonstra- tion is given to show that the solution was correct . This does not appear to me to be in the line of discovery . I have in all cases started with a ...
Σελίδα ix
... Problems in Construction BOOK III . RATIO AND PROPORTION . SIMILAR FIGURES . Definitions Proportional Lines . Similar Polygons 888 78 84 87 BOOK IV . AREAS OF POLYGONS . Definitions Problems in ix.
... Problems in Construction BOOK III . RATIO AND PROPORTION . SIMILAR FIGURES . Definitions Proportional Lines . Similar Polygons 888 78 84 87 BOOK IV . AREAS OF POLYGONS . Definitions Problems in ix.
Σελίδα x
James Howard Gore. BOOK IV . AREAS OF POLYGONS . Definitions Problems in Construction BOOK V. REGULAR POLYGONS AND CIRCLES . Definitions Maxima and Minima SOLID GEOMETRY . BOOK VI . PLANES AND SOLID ANGLES . Definitions Diedral Angles ...
James Howard Gore. BOOK IV . AREAS OF POLYGONS . Definitions Problems in Construction BOOK V. REGULAR POLYGONS AND CIRCLES . Definitions Maxima and Minima SOLID GEOMETRY . BOOK VI . PLANES AND SOLID ANGLES . Definitions Diedral Angles ...
Σελίδα 2
... Problem is a question proposed for solution . 15. A Postulate assumes the possibility of the solution of some problem . 16. An Axiom is a truth assumed to be true , or a truth veri- fied by intuition or our experience with material ...
... Problem is a question proposed for solution . 15. A Postulate assumes the possibility of the solution of some problem . 16. An Axiom is a truth assumed to be true , or a truth veri- fied by intuition or our experience with material ...
Σελίδα 3
... problem is the method of construction which accomplishes the required end . 24. A Construction is the drawing of such lines and curves as may be required to prove the truth of a theorem , or to solve a problem . 25. The Enunciation of a ...
... problem is the method of construction which accomplishes the required end . 24. A Construction is the drawing of such lines and curves as may be required to prove the truth of a theorem , or to solve a problem . 25. The Enunciation of a ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC² acute angle AD² adjacent adjacent angles altitude angle formed angles are equal apothem arc BC base and altitude bisect bisector called centre chord circumference circumscribed cone cylinder diagonals diameter diedral angles distance divided draw drawn ECDH equally distant equilateral equivalent EXERCISES faces four right angles frustum given point given straight line hence homologous homologous sides hypotenuse inscribed polygon interior angles intersection isosceles triangle join lateral area lateral edges Let ABC lune mean proportional measured by one-half middle point number of sides parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron PROPOSITION XI prove pyramid Q.E.D. PROPOSITION quadrilateral radii radius ratio rectangle rectangular parallelopiped regular polygon right triangle SCHOLIUM segments semiperimeter sphere spherical angle spherical polygon spherical triangle surface tangent THEOREM triangle ABC triangles are equal triangular triangular prism V-ABC vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 46 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Σελίδα 105 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Σελίδα 82 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Σελίδα 192 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 108 - Two triangles having 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 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Σελίδα 30 - In an isosceles triangle, the angles opposite the equal sides are equal.
Σελίδα 80 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Σελίδα 79 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.
Σελίδα 148 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.