An Elementary Treatise on the Geometrical and Algebraical Investigation of Maxima and Minima: Being the Substance of a Course of Lectures Delivered Conformably to the Will of Lady Sadler : to which is Added A Selection of Propositions Deducible from Euclid's Elements |
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Häufige Begriffe und Wortgruppen
aggregate arch base bisected body Book chord circumference coefficients common construction demonstration denote derivative described determine diameter difference distance divided double draw equal equation equiangular equilateral triangle EXAMPLE expansion extremities fall figure find a point former four function Geometry given circle given point given straight line greater ratio greatest half Hence horizontal inscribed isosceles triangle join latter least less lines be drawn magnitude manifest manner maximum mean meet number of sides opposite parallel parallelogram pass perimeter perpendicular placed plane polygon positive powers prism Problem produced PROP proportional proposition proved quantity rectangle contained rectilineal figure regular polygon remaining right angles sector segment shewn similar square standing supposed surface taken tangent terminated Theorem third touch vertical angle wherefore whole
Beliebte Passagen
Seite 81 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 83 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Seite 56 - 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...
Seite 36 - In every triangle, the square of the side subtending any of the acute angles is less than the squares of the sides containing that angle by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular...
Seite 32 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Seite 85 - Divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part.
Seite 12 - If two triangles have the three angles of one equal to the three angles of the other, each to each, do you think the two triangles are necessarily alike in every respect ? 5.
Seite 16 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Seite 154 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 22 - If from the right angle of a right-angled triangle, two straight lines be drawn, one perpendicular to the base, and the other bisecting it, they will contain an angle equal to the difference of the two acute angles of the triangle.
Bibliografische Informationen
| Titel | An Elementary Treatise on the Geometrical and Algebraical Investigation of Maxima and Minima: Being the Substance of a Course of Lectures Delivered Conformably to the Will of Lady Sadler : to which is Added A Selection of Propositions Deducible from Euclid's Elements |
| Autor/in | Daniel Cresswell |
| Ausgabe | 2 |
| Verlag | J. Smith, 1817 |
| Original von | University of Michigan |
| Digitalisiert | 19. Okt. 2007 |
| Länge | 436 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |