## 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 |

### From inside the book

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Page 17

... triangles pass . Draw ( Art . 2. ) the base FG such that it shall be bisected in D , and let BDC be the base of any other of the triangles ; the tri- angle AFG is less than the

... triangles pass . Draw ( Art . 2. ) the base FG such that it shall be bisected in D , and let BDC be the base of any other of the triangles ; the tri- angle AFG is less than the

**triangle ABC**. Through G , the extremity of FG which is not ... Page 18

... triangles MKC , LBK , and is the half of the whole tri- angle ABC . In the same manner the parallelo- gram AD may be shewn to be half of the triangle AFG : but ( Art . 3. ) the

... triangles MKC , LBK , and is the half of the whole tri- angle ABC . In the same manner the parallelo- gram AD may be shewn to be half of the triangle AFG : but ( Art . 3. ) the

**triangle ABC**is greater than the triangle AFG ; therefore ... Page 19

...

...

**ABC**, and angle NPK to the angle ACB ( E. 29. 1 ) , and also to the angle DKB ; wherefore the four angles DBK , DKB , EKC , ECK are equal to each other ; and the side DK of the**triangle**BDK is , by the hypothesis , equal to the side KE ... Page 21

... triangle AEC . But the

... triangle AEC . But the

**triangle ABC**is greater than the triangle AEC , because BC has been shewn to be greater than EC ; therefore the**triangle ABC**is greater than the triangle ADC . 9. COR . 1. A square is greater than given ... Page 24

...

...

**triangle**ACG is greater than the**triangle**ACE , if to the former be added the figures**ABC**and CHG , and to the latter the figures**ABC**and CDE , which has been shewn to be equal to CHG , it is manifest that the whole figure ABCHG is ...### Other editions - View all

An Elementary Treatise on the Geometrical and Algebraical Investigation of ... Daniel Cresswell No preview available - 2016 |

An Elementary Treatise on the Geometrical and Algebraical Investigation of ... D. Cresswell No preview available - 2015 |

An Elementary Treatise on the Geometrical and Algebraical Investigation of ... D 1776-1844 Cresswell No preview available - 2015 |

### Common terms and phrases

ABCD aggregate Algebra altitude angle equal apparent magnitude base Binomial Theorem bisected chord circumference coefficients Cx² derivative describe a circle diameter divided double draw a straight equal perimeter equation equilateral triangle Euclid Euclid's Elements find a point finite straight line function Geometry given angle given circle given finite straight given point given ratio given straight line given triangle greater ratio greatest hypotenuse inscribed isosceles triangle less Let ABC lines be drawn magnitudes MAXIMA AND MINIMA maximum minimum number of sides parallel parallelepiped parallelogram plane prism produced PROP proposition quadrilateral rectilineal figure rectangle contained regular polygon rhomb right angles right-angled triangle scalene triangle SCHOLIUM sector segment shewn square straight line drawn straight line joining subtended tangent Theorem trapezium triangle ABC variable quantity velocity vertex vertical angle wherefore

### Popular passages

Page 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.

Page 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'.

Page 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...

Page 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...

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.