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" The pupil will be much helped in the study of solid geometry by noticing that most of the theorems are but extensions or generalizations of theorems previously studied in the plane geometry. 437. The relations of the parts of a figure or figures in a... "
Solid Geometry - Page 289
by George C. Shutts - 1913
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...be classified as elementary and composite. INTRODUCTION. 4. A plane surface, or simply a plane, is a surface such that the straight line joining any two of its points lies wholly in the surface. 5. Plane surfaces are classified with reference to their bounding lines, as...
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...CHAPTER XII. PLANES AND THEIR ANGLES. DEFINITIONS. 1. A Plane (or Plane Surface), as already defined, is a surface such that the straight line joining any two of its points lies wholly in the surface. Note-—To ascertain whether a given surface is a plane, apply the straight...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...YEDRAL ANGLES. DEFINITIONS AND GENERAL PRINCIPLES. 416. In § 10 a plane surface was defined as one such that the straight line joining any two of its points lies entirely in the surface. Thus the surface MN is a plane if •>£ -7 the straight line AB joining any two / , / of its points...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...straight line be drawn between the points J.and B. This line must lie in MN, and also in PQ. [A plane is a surface such that the straight line joining any two of its points lies entirely in the surface.] (§ 8.) Then it must be the intersection of MN and PQ. Whence, AB is a straight line. 397. DBF. If...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 250 pages
...word " line " will be used hereafter as signifying a straight line. 9. A plane surface, or plane, is a surface such that the straight line joining any two of its points lies entirely in the surface. Thus, if P and Q are any two points in surface MN, and the straight line joining P and Q lies entirely...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...word " line " will be used hereafter as signifying a straight line. 9. A plane surface, or plane, is a surface such that the straight line joining any two of its points _jf lies entirely in the surface. Thus, if P and Q are any two points in / p~ surface MN, and the straight...
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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 336 pages
...plane of the lines AD, BD, and CD, AB lies in this plane. [A plane is a surface such that the str. line joining any two of its points lies entirely in the surface.] (§ 0) 1. That is, AB and CD lie in the same plane. 8. Again, AB and CD are JL BD. [A J. to a plane...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...broken line is composed of a succession of straight lines. EF is a broken line. SURFACES. 16. A plane is a surface such that the straight line, joining any two of its points, lies wholly in the surface. 17. A curved surface is a surface, no portion of which, however small, is a...
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1912 - 392 pages
...435. Adapt the demonstration § 434 to theorem § 433. SOLID GEOMETRY. CHAPTER VII. LINES AND PLANKS 436. SOLID GEOMETRY. That portion of Geometry which...the line lies wholly in the plane. 439. INTERSECTION OP PLANES. That portion of two planes which is common to both is their intersection. 440. PLANE DETERMINED....
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1912 - 392 pages
...assumption in step 2 is false. c 5. Similarly prove that — cannot be c' less than — r' Therefore — SOLID GEOMETRY. CHAPTER VII. LINES AND PLANES 436....from the definition it follows that if a straight lino of a plane be indefinitely extended, it can never leave the plane. A plane embraces a line, or...
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