The Elements of Plane and Solid Geometry ...D. Van Nostrand Company, 1890 - 393 σελίδες |
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Σελίδα iii
... proof . Each assertion in the proof begins a new line , and is accompanied by a reference to the preced- ing principle on which the assertion depends . These references are quoted two or three times in small type , and afterwards ...
... proof . Each assertion in the proof begins a new line , and is accompanied by a reference to the preced- ing principle on which the assertion depends . These references are quoted two or three times in small type , and afterwards ...
Σελίδα 10
... proof . 31. A problem is a question which requires solution , such as a particular line to be drawn , or a required figure to be constructed . 32. An axiom is a self - evident truth , which is admitted without proof . 33. A postulate ...
... proof . 31. A problem is a question which requires solution , such as a particular line to be drawn , or a required figure to be constructed . 32. An axiom is a self - evident truth , which is admitted without proof . 33. A postulate ...
Σελίδα 17
... Proof . < AEC BED . CEA + ≤ CEB = 2 rt . ≤s , being sup . adj . ≤8 ( 52 ) . AEC + AED = 2 rt . LS , being sup . adj . 48 ( 52 ) . :: 2 CEA + △ CEB = △ AEC + AED . All rt . 8 are equal to one another ( 49 ) . Take away the common ...
... Proof . < AEC BED . CEA + ≤ CEB = 2 rt . ≤s , being sup . adj . ≤8 ( 52 ) . AEC + AED = 2 rt . LS , being sup . adj . 48 ( 52 ) . :: 2 CEA + △ CEB = △ AEC + AED . All rt . 8 are equal to one another ( 49 ) . Take away the common ...
Σελίδα 18
... Proof . Let the part of the plane above the line AB , and which con- tains P , be revolved about AB as an axis until the point P comes into the position P ' . A- P с D Then , since ACP is a rt . 2 , Z ACP ' is also a rt . . ( 29 ) If ...
... Proof . Let the part of the plane above the line AB , and which con- tains P , be revolved about AB as an axis until the point P comes into the position P ' . A- P с D Then , since ACP is a rt . 2 , Z ACP ' is also a rt . . ( 29 ) If ...
Σελίδα 20
... Proof . Produce BD to meet AC at E. Then BA + AE > BE . ( Ax . 10 ) Add EC to each . ... BA + AC > BE + EC . ( Ax ... proof of the second part of Prop . 4 , that the angle AEC is equal to the angle BED . 2. Prove that the straight line ...
... Proof . Produce BD to meet AC at E. Then BA + AE > BE . ( Ax . 10 ) Add EC to each . ... BA + AC > BE + EC . ( Ax ... proof of the second part of Prop . 4 , that the angle AEC is equal to the angle BED . 2. Prove that the straight line ...
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Άλλες εκδόσεις - Προβολή όλων
ELEMENTS OF PLANE & SOLID GEOM Edward a. (Edward Albert) 1845 Bowser Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
ELEMENTS OF PLANE & SOLID GEOM Edward a. (Edward Albert) 1845 Bowser Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude angles are equal base bisect bisector centre chord circumference circumscribed coincide cone of revolution Cons construct cylinder diagonals diameter diedral angle distance divided draw equally distant equilateral triangle equivalent EXERCISES exterior angle faces feet Find the area Find the volume frustum given circle given line given point given straight line homologous homologous sides hypotenuse inches intersection isosceles triangle lateral area lateral edges Let ABC meet middle point number of sides parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced Proposition Proposition 13 prove Proof pyramid quadrilateral radii radius ratio rectangle rectangular parallelopiped regular inscribed regular polygon right angles segment similar slant height sphere spherical polygon spherical triangle square surface symmetrical tangent tetraedron Theorem triangle ABC triangular prism triedral vertex
Δημοφιλή αποσπάσματα
Σελίδα 74 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Σελίδα 188 - 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 45 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Σελίδα 137 - Terms of the proportion. The first and fourth terms are called the Extremes, and the second and third the Means.
Σελίδα 12 - AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums will be equal.
Σελίδα 57 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Σελίδα 334 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Σελίδα 253 - 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.
Σελίδα 378 - The circumferences of the sections made by the planes are called the bases of the zone, and the distance between the planes is the altitude of the zone.