Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 σελίδες |
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Αποτελέσματα 1 - 5 από τα 70.
Σελίδα 16
... bisect . In the side AB take any point D , and from BC cut off BE equal to BD ; join DE , on which construct ( I. 1 ... bisects it must be the per- pendicular required . Taking BD , therefore , equal to BE , and A D B EC ...
... bisect . In the side AB take any point D , and from BC cut off BE equal to BD ; join DE , on which construct ( I. 1 ... bisects it must be the per- pendicular required . Taking BD , therefore , equal to BE , and A D B EC ...
Σελίδα 17
... equal ; these subordinate triangles are ( I. 3. ) equal , and consequently the angle DGC is equal to DGF , and each of them a right angle , or CG is per- pendicular to AB . C PROP . VII . PROB . To bisect a given BOOK I. 17.
... equal ; these subordinate triangles are ( I. 3. ) equal , and consequently the angle DGC is equal to DGF , and each of them a right angle , or CG is per- pendicular to AB . C PROP . VII . PROB . To bisect a given BOOK I. 17.
Σελίδα 18
... bisect a given finite straight line . On the given straight line AB , construct two isosceles triangles ( I. 1. ) ACB and ADB , and join their vertices C and D by a straight line cutting AB in the point E : AB is bisected in E. For the ...
... bisect a given finite straight line . On the given straight line AB , construct two isosceles triangles ( I. 1. ) ACB and ADB , and join their vertices C and D by a straight line cutting AB in the point E : AB is bisected in E. For the ...
Σελίδα 20
... bisecting the vertical angle ABC . Because , by hypothesis , AB is equal to BC , the side BD common to the two tri- angles BDA and BDC , and the angles ABD and CBD contained by them are equal ; these triangles are equal ( I. 3. ) , and ...
... bisecting the vertical angle ABC . Because , by hypothesis , AB is equal to BC , the side BD common to the two tri- angles BDA and BDC , and the angles ABD and CBD contained by them are equal ; these triangles are equal ( I. 3. ) , and ...
Σελίδα 48
... bisects the rhomboid DEFC ( I. 26. cor . ) , and the triangles DBC and DEC , having DC the same altitude , are equivalent ( II . 1. ) ; consequently their doubles , or the triangle ABC and ... bisect the base 48 ELEMENTS OF GEOMETRY .
... bisects the rhomboid DEFC ( I. 26. cor . ) , and the triangles DBC and DEC , having DC the same altitude , are equivalent ( II . 1. ) ; consequently their doubles , or the triangle ABC and ... bisect the base 48 ELEMENTS OF GEOMETRY .
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Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angle altitude angle ABC angle ADB angle BAC angle BCD base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle Geometry greater half Hence hypotenuse inscribed intercepted isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter side AC sides AB sinAC sinB sine square of AB square of AC tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 30 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Σελίδα 333 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Σελίδα 294 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Σελίδα 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 137 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Σελίδα 84 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Σελίδα 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Σελίδα 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Σελίδα 38 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.