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 29.
Σελίδα 55
... excess of the square of CF above that of CD is equivalent to the square of DF , or the square of DF is equivalent to the excess of the square of A above that of B. PROP . XIV , THEOR . The rectangle contained by BOOK II . 55.
... excess of the square of CF above that of CD is equivalent to the square of DF , or the square of DF is equivalent to the excess of the square of A above that of B. PROP . XIV , THEOR . The rectangle contained by BOOK II . 55.
Σελίδα 57
... excess of the two squares of AB and BC above twice their rectangle . For let the squares of AB , BC and AC be completed , and produce CE and DE the sides of the latter to H and I. H D E It is evident , that GE is BOOK IL 57.
... excess of the two squares of AB and BC above twice their rectangle . For let the squares of AB , BC and AC be completed , and produce CE and DE the sides of the latter to H and I. H D E It is evident , that GE is BOOK IL 57.
Σελίδα 58
... excess of the square of AB above that of BC . For , having made AG equal to AC , draw GH parallel to AD ( I. 23. ) , and CI , DH parallel to AE . E I F Because GK is equal to KC or HD , and EG is equal to CB or BD , the rectangle EK is ...
... excess of the square of AB above that of BC . For , having made AG equal to AC , draw GH parallel to AD ( I. 23. ) , and CI , DH parallel to AE . E I F Because GK is equal to KC or HD , and EG is equal to CB or BD , the rectangle EK is ...
Σελίδα 59
... excess of the square of AC above that of CD , and consequently the rectangle AD , DB , with the square of CD , is equal to the square of AC . A Cor . 2. If a straight line AB be bisected in C and pro- duced to D , the rectangle ...
... excess of the square of AC above that of CD , and consequently the rectangle AD , DB , with the square of CD , is equal to the square of AC . A Cor . 2. If a straight line AB be bisected in C and pro- duced to D , the rectangle ...
Σελίδα 65
... excess of the of AB above that of BC is equivalent to the excess of the square of AE above square B that of CE . But the excess of the square of AE above that of CE , is ( II . 17. ) equivalent to the rectangle con- DE tained by their ...
... excess of the of AB above that of BC is equivalent to the excess of the square of AE above square B that of CE . But the excess of the square of AE above that of CE , is ( II . 17. ) equivalent to the rectangle con- DE tained by their ...
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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 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 given greater half Hence hypotenuse inscribed 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 sine square of AC squares of AB straight line 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.