Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and IllustrationsJames Ballantyne and Company, 1809 - 493 páginas |
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Página 3
... divided into Plane and Solid ; the former confining its views to the properties of space delineated on the same plane ; the latter embracing the relations of different planes or surfaces , and of the solids which these describe or ...
... divided into Plane and Solid ; the former confining its views to the properties of space delineated on the same plane ; the latter embracing the relations of different planes or surfaces , and of the solids which these describe or ...
Página 39
... divided in these points into five equal parts . E N M AHIK LB For draw DM , EN , FO , and GP parallel to AB . And because DH is parallel to EM , the exterior angle ADH is equal to DEM ( I. 25. ) ; and for the same reason , since AH is ...
... divided in these points into five equal parts . E N M AHIK LB For draw DM , EN , FO , and GP parallel to AB . And because DH is parallel to EM , the exterior angle ADH is equal to DEM ( I. 25. ) ; and for the same reason , since AH is ...
Página 44
... The triangle ABC is thus divided into four equivalent triangles , of which DBE is one . , Hence also the rhomboid GDEC is half of the original triangle . PROP . V. THEOR . Straight lines joining the successive 44 ELEMENTS OF GEOMETRY .
... The triangle ABC is thus divided into four equivalent triangles , of which DBE is one . , Hence also the rhomboid GDEC is half of the original triangle . PROP . V. THEOR . Straight lines joining the successive 44 ELEMENTS OF GEOMETRY .
Página 57
... them and the several segments into which the other is divided . • The rectangle under AC and AB , is equivalent to the rectangles contained by AC and the segments AD , DE , and EB . For through the points D and E draw DF and BOOK II . 57.
... them and the several segments into which the other is divided . • The rectangle under AC and AB , is equivalent to the rectangles contained by AC and the segments AD , DE , and EB . For through the points D and E draw DF and BOOK II . 57.
Página 61
... divided equally and unequally , the rectangle contained by the unequal seg- ments is equivalent to the difference of the squares of the half line and of the interval between the points of section . 1 The PROP . XXIV . THEOR . square ...
... divided equally and unequally , the rectangle contained by the unequal seg- ments is equivalent to the difference of the squares of the half line and of the interval between the points of section . 1 The PROP . XXIV . THEOR . square ...
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Términos y frases comunes
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
Pasajes populares
Página 460 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Página 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.
Página 145 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Página 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.
Página 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.
Página 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...
Página 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.
Página 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.
Página 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...
Página 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.