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 26
... extended from C to AB , making on the same side , the one an obtuse angle CEA , and the other an acute angle CFA . As the term distance signifies the shortest road , the distance between two points is the straight line which joins them ...
... extended from C to AB , making on the same side , the one an obtuse angle CEA , and the other an acute angle CFA . As the term distance signifies the shortest road , the distance between two points is the straight line which joins them ...
Página 28
... extended line AB towards A , and will in ils progress afterwards meet the same line on the other side towards B. In the position IFH , the angle EFH is the exterior angle of the triangle FHG , and therefore greater than FGH or EGA ( I ...
... extended line AB towards A , and will in ils progress afterwards meet the same line on the other side towards B. In the position IFH , the angle EFH is the exterior angle of the triangle FHG , and therefore greater than FGH or EGA ( I ...
Página 54
... extended to any number of squares . A E B PROP . XVII . PROB . To find the side of a square equivalent to the dif- ference between two given squares . Let A and B be the sides of two squares ; it is required to find a square equivalent ...
... extended to any number of squares . A E B PROP . XVII . PROB . To find the side of a square equivalent to the dif- ference between two given squares . Let A and B be the sides of two squares ; it is required to find a square equivalent ...
Página 79
... extend the straight line to terminate both ways in the circumference at A and B. Because Ċ is the centre of the circle , AC is equal to CB ; but since E A B C D F D is also a centre , AD must be equal to DE ; that is , a greater to a ...
... extend the straight line to terminate both ways in the circumference at A and B. Because Ċ is the centre of the circle , AC is equal to CB ; but since E A B C D F D is also a centre , AD must be equal to DE ; that is , a greater to a ...
Página 96
... each side of any point in the circumference of a circle , equal arcs be repeated ; the chords which join the opposite points of section will be together equal to the last chord extended till it meets a 3 96 ELEMENTS OF GEOMETRY .
... each side of any point in the circumference of a circle , equal arcs be repeated ; the chords which join the opposite points of section will be together equal to the last chord extended till it meets a 3 96 ELEMENTS OF GEOMETRY .
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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 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
Pasajes populares
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 147 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Página 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
Página 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...
Página 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.
Página 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.
Página 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.
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 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.
Página 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.