Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and IllustrationsJames Ballantyne and Company, 1809 - 493 sider |
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Side 20
With an Appendix, Notes and Illustrations Sir John Leslie. Cor . Hence from any point only one straight line can be drawn , making a given angle on the same side with a given straight line ; and hence also no more than one per ...
With an Appendix, Notes and Illustrations Sir John Leslie. Cor . Hence from any point only one straight line can be drawn , making a given angle on the same side with a given straight line ; and hence also no more than one per ...
Side 26
... Hence only a single perpendicular CD can be let fall from the same point C upon a given straight line AB ; and hence also a pair only of equal straight lines greater than CD can at once be extended from C to AB , making on the same side ...
... Hence only a single perpendicular CD can be let fall from the same point C upon a given straight line AB ; and hence also a pair only of equal straight lines greater than CD can at once be extended from C to AB , making on the same side ...
Side 31
... Hence the angles of a square or rectangle are all of them right angles ; for the opposite sides , being equal , are ... Hence the diagonal divides a rhomboid or paral- lelogram into two equal triangles . Hence also an oblong is a ...
... Hence the angles of a square or rectangle are all of them right angles ; for the opposite sides , being equal , are ... Hence the diagonal divides a rhomboid or paral- lelogram into two equal triangles . Hence also an oblong is a ...
Side 34
... Hence the two acute angles of a right angled tri- angle are together equal to one right angle ; and hence each angle of an equilateral triangle is two third parts of a right angle . Cor . 2. Hence if a triangle have its exterior angle ...
... Hence the two acute angles of a right angled tri- angle are together equal to one right angle ; and hence each angle of an equilateral triangle is two third parts of a right angle . Cor . 2. Hence if a triangle have its exterior angle ...
Side 36
... Hence the angles EFG , DEH , CDI , ABL , FAM diminished by BCK are equal to four right angles . I B K C F E PROP . XXXVII . THEOR . If the opposite angles of a quadrilateral figure be equal , its opposite sides will be likewise equal ...
... Hence the angles EFG , DEH , CDI , ABL , FAM diminished by BCK are equal to four right angles . I B K C F E PROP . XXXVII . THEOR . If the opposite angles of a quadrilateral figure be equal , its opposite sides will be likewise equal ...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... Sir John Leslie Uten tilgangsbegrensning - 1811 |
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... Sir John Leslie Uten tilgangsbegrensning - 1811 |
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... Sir John Leslie Uten tilgangsbegrensning - 1811 |
Vanlige uttrykk og setninger
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 drawn equal to BC exterior angle fall the perpendicular given angle 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 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 AB square of AC tangent THEOR triangle ABC twice the square vertex vertical angle whence wherefore
Populære avsnitt
Side 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.
Side 147 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Side 92 - 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
Side 458 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Side 99 - ... a circle. The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary; and the converse.
Side 155 - 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.
Side 408 - 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.
Side 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...
Side 36 - 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.
Side 60 - 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.