Modern geometry [ed.] with an appendix by W.B. Jack1876 |
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Side iii
... chapter are made introductory to the strictly logical demonstrations , and are printed in smaller type , to prevent ... chapters the logical relationship of the propositions is thoroughly examined and different ways of stating certain ...
... chapter are made introductory to the strictly logical demonstrations , and are printed in smaller type , to prevent ... chapters the logical relationship of the propositions is thoroughly examined and different ways of stating certain ...
Side v
... CHAPTER I. LINES AND PLANES . Definition. CHAP . I. Lines and Planes . Definition Surfaces - Lines - Points - Straight Lines - The Vertical- A Moving Point - Plane Surfaces - The Horizon- tal - Intersection of Sur- face Planes - Surfaces ...
... CHAPTER I. LINES AND PLANES . Definition. CHAP . I. Lines and Planes . Definition Surfaces - Lines - Points - Straight Lines - The Vertical- A Moving Point - Plane Surfaces - The Horizon- tal - Intersection of Sur- face Planes - Surfaces ...
Side 1
Richard Wormell W Brydone Jack. MODERN GEOMETRY . CHAPTER I. LINES AND PLANES . Definition . The object of the science of Geometry , is to investigate those properties of bodies which have relation to space . The foundation of the ...
Richard Wormell W Brydone Jack. MODERN GEOMETRY . CHAPTER I. LINES AND PLANES . Definition . The object of the science of Geometry , is to investigate those properties of bodies which have relation to space . The foundation of the ...
Side 10
... extremities of these straight lines . ( i ) . Measure the lengths of the three straight lines , and express them as nearly as possible in inches and parts of an inch . CHAPTER II . ANGLES . IN the previous Chapter , 10 MODERN GEOMETRY .
... extremities of these straight lines . ( i ) . Measure the lengths of the three straight lines , and express them as nearly as possible in inches and parts of an inch . CHAPTER II . ANGLES . IN the previous Chapter , 10 MODERN GEOMETRY .
Side 11
Richard Wormell W Brydone Jack. CHAPTER II . ANGLES . IN the previous Chapter , the properties of a straight line are investi- gated ; we have now to consider different ways in which two straight lines can be drawn from the same point ...
Richard Wormell W Brydone Jack. CHAPTER II . ANGLES . IN the previous Chapter , the properties of a straight line are investi- gated ; we have now to consider different ways in which two straight lines can be drawn from the same point ...
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Modern Geometry [Ed.] with an Appendix by W.B. Jack Richard Wormell Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
A B and C D A B C D adjacent angles alternate angles angles equal angular points base bisector centre chord circumference circumscribing circle Construct a triangle contra-positive converse decagon describe a circle diameter distance divided draw a straight extremities figure fixed point fulfils the given given angle given circle given condition given straight line gonals greater Hence hypothenuse inches inscribed inscribed angle inscribed circle interior angles isosceles triangle less Let A B C line A B locus of points magnitudes middle points number of sides opposite angles opposite sides parallel parallelogram perpendicular point of contact point of intersection PROBLEM propositions proved quadrilateral ratio rect rectangle contained regular polygon respectively equal rhombus right angles right-angled triangle segment semicircle side opposite square on A B tangent termed Theo THEOREMS ON CHAPTER triangles are equal vertical angle
Populære avsnitt
Side 242 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 240 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 240 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 242 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Side 242 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.
Side 241 - If the first has to the second the same ratio which the third has to the fourth...
Side 240 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 242 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Side 239 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.