Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and Illustrations |
From inside the book
Results 1-5 of 78
Page viii
... third Books are almost wholly occu- pied with the researches of the Ancient Analysis . In framing them , I have consulted a great variety of authors , some of whom are of difficult access . The labour of condensing the scattered ...
... third Books are almost wholly occu- pied with the researches of the Ancient Analysis . In framing them , I have consulted a great variety of authors , some of whom are of difficult access . The labour of condensing the scattered ...
Page 3
... third point . The separation or opening of two straight lines at their point of intersection , constitutes an angle . If we obtain the idea of distance , or linear extent , from progressive motion , we derive that of diver- gence , or ...
... third point . The separation or opening of two straight lines at their point of intersection , constitutes an angle . If we obtain the idea of distance , or linear extent , from progressive motion , we derive that of diver- gence , or ...
Page 7
... will be shown ( I. 12. ) that every triangle has at least two acute angles . The third angle may , therefore , by its character serve to discriminate a triangle . 18. A right - angled triangle is that which has BOOK 1 . 7.
... will be shown ( I. 12. ) that every triangle has at least two acute angles . The third angle may , therefore , by its character serve to discriminate a triangle . 18. A right - angled triangle is that which has BOOK 1 . 7.
Page 13
... third sides AC and DF are equal , and the angles BAC , BCA opposite to BC and BA are equal respectively to EDF and EFD , which the corre- sponding sides EF and ED subtend . PROP . IV . PROB . At a point in a straight line , to make an ...
... third sides AC and DF are equal , and the angles BAC , BCA opposite to BC and BA are equal respectively to EDF and EFD , which the corre- sponding sides EF and ED subtend . PROP . IV . PROB . At a point in a straight line , to make an ...
Page 21
... third AC . PROP . XVII . THEOR . 1 The difference between two sides of a triangle is less than the third side . Let the side AC be greater than AB , and from it cut off a part AE equal to AB ; the remain- der EC is less than the third ...
... third AC . PROP . XVII . THEOR . 1 The difference between two sides of a triangle is less than the third side . Let the side AC be greater than AB , and from it cut off a part AE equal to AB ; the remain- der EC is less than the third ...
Other editions - View all
Common terms and phrases
ABCD ANALYSIS angle ABC angle ACB angle BAC bisect centre chord circumference COMPOSITION conse consequently the angle decagon describe a circle diameter distance diverging lines draw drawn equal to BC evidently exterior angle fall the perpendicular given circle given in position given point given ratio given space given straight line greater hence hypotenuse inflected inscribed intercepted intersection isosceles triangle join let fall likewise mean proportional parallel perpendicular point F polygon porism PROB PROP quently radius rectangle rectangle contained regular polygon rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter sequently side AC similar sine square of AC squares of AB tangent THEOR triangle ABC twice the square vertex vertical angle whence wherefore
Popular passages
Page 460 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Page 28 - ... 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.
Page 145 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Page 34 - 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.
Page 153 - 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.
Page 16 - PROP. V. THEOR. The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced, the angles -upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC, be produced to D and E: the angle ABC shall be equal to the angle ACB, and the angle...
Page 411 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 58 - Prove, geometrically, that the rectangle of the sum and the difference of two straight lines is equivalent to the difference of the squares of those lines.
Page 64 - IF a straight line be bisected, and produced to any point: the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Page 157 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.