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 viii
... problems , rising above each other in gradual succession . The second and 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 ...
... problems , rising above each other in gradual succession . The second and 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 ...
Side ix
... problem is of essential consequence in marine surveying . Having already exceeded the ordinary limits , it perhaps unfortunately became requisite to curtail the Notes and Illustrations , with which the volume concludes PREFACE . ix.
... problem is of essential consequence in marine surveying . Having already exceeded the ordinary limits , it perhaps unfortunately became requisite to curtail the Notes and Illustrations , with which the volume concludes PREFACE . ix.
Side x
... problems relative to trigonometry and geodesiacal operations , in which the modern analysis is sparingly introdu ced , are of a nature sufficiently interesting , I would presume , to claim the notice of proficients in sci- ence . The ...
... problems relative to trigonometry and geodesiacal operations , in which the modern analysis is sparingly introdu ced , are of a nature sufficiently interesting , I would presume , to claim the notice of proficients in sci- ence . The ...
Side 10
... problem or a theorem . A PROBLEM proposes to effect some combination . A THEOREM advances some truth , which is to be esta- blished . A problem requires solution , a theorem wants demonstra- tion ; the former implies an operation , and ...
... problem or a theorem . A PROBLEM proposes to effect some combination . A THEOREM advances some truth , which is to be esta- blished . A problem requires solution , a theorem wants demonstra- tion ; the former implies an operation , and ...
Side 11
... problem . Corollary . If the radii G and H be equal to each other , the triangle will evidently be isosceles ; and if those lines be likewise equal to the base AB , the triangle must be equilateral . PROP . II . THEOREM . Two triangles ...
... problem . Corollary . If the radii G and H be equal to each other , the triangle will evidently be isosceles ; and if those lines be likewise equal to the base AB , the triangle must be equilateral . PROP . II . THEOREM . Two triangles ...
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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 - 1809 |
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 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
Populære avsnitt
Side 460 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
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 145 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Side 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.
Side 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.
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 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.
Side 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.
Side 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...
Side 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.