# A Course of Mathematics ...:

For the Use of Academies, as Well as Private Tuition, Volume 1 (Google eBook)
Samuel Campbell, 1812 - Mathematics

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### Contents

 Principles 1 RomanNotation 8 Reduction 23 Compound Addition 32 Multiplication 38 Golden Rule or Rule of Three 44 Vulgar Fractions 51 Addition of Vulgar Fractions 61
 Surds 206 Infinite Series 213 Piling of Balls 223 Simple Equations 230 Quadratic Equations 249 Resolutionof Cubic and Higher EgtuUions 257 Simple Inaerest 266 GEOMETRY 290

 Reductionof decimals74 65 Addition of Decimals 67 CONTENTS 77 To extract the Cube Root 85 RatiosProportions and Progressions 110 Geometrical Progression 116 Double Fellowship 188 122 JUtigation Medial 129 Single Position 135 Practical Questions ISO 150 To compute logarithms 159 Multiplication by Logarithms 168 Definitions and Notation 171 Subtraction 180 Algebraic Fractions 188 Involution 199
 Definitions 275 319 AxiomsTheorems 281 336 Problems 352 Applications of Algebra to Geometry 369 Plane Trigonometry 377 Heights and Distances 393 Mensuration of planes408 402 Mensuration of SoUds 419 land 429 Land Siirveymg 439 Artificers Works 457 Conic Sections 469 Of the Parabola 514 Of the Conic sectionsas expressed by Algebraic equations called 532 problemsrelative to the Div sion of Surfaces 558 Construction of Geometrical Problems 571

### Popular passages

Page 291 - 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.
Page 4 - Los números cardinales 0: zero 1: one 2: two 3: three 4: four 5: five 6: six 7: seven 8: eight 9: nine 10: ten 11: eleven 12: twelve 13: thirteen 14: fourteen 15: fifteen 16: sixteen 17: seventeen 18: eighteen 19: nineteen 20: twenty...
Page 2 - The sum of the three angles of any triangle is equal to two right angles, this is a Theorem, the truth of which is demonstrated by Geometry.
Page 320 - Proportion, when the ratio is the same between every two adjacent terms, viz. when the first is to the second, as the second to the third, as the third to the fourth, as the fourth to the fifth, and so on, all in the same common ratio.
Page 301 - In any triangle, the difference of the squares of the two sides w equal to the difference of the squares of the segments of the base, or of the two lines or distances included between the extremes of the base and the perpendicular.
Page 170 - When the index of the logarithm to be divided is negative, and does not exactly contain the divisor without some remainder, increase the index by such a number as will make it exactly divisible by the index, carrying the units borrowed, as so many tens, to the left-hand place of the decimal, and, then divide as in whole numbers. EXAMPLES. 1.
Page 312 - The angle formed by a tangent to a circle, and a chord drawn from the point of contact, is equal to the angle in the alternate segment.
Page 377 - The Circumference of every circle is supposed to be divided into 360 equal parts, called Degrees ; and each degree into 60 Minutes, each minute into 60 Seconds, and so on. Hence a semicircle contains 180 degrees, and a quadrant 90 degrees. 58. The Measure of an angle is an arc of any circle contained between the two lines which form that angle, the angular point being the centre ; and it is estimated by the number of degrees contained in that arc.
Page 458 - BRICKLAYERS- WORK. — Brickwork is estimated at the rate of a brick and a half thick. So that, if a wall be more or less than this standard thickness, it must be reduced to it, as follows : — Multiply the superficial content of the wall by the number of half bricks in the thickness, and divide the product by 3. The...
Page 319 - Three quantities are said to be proportional when the ratio of the first to the second is equal to the ratio of the second to the third.

### References from web pages

Thomas Stephens Davies - Wikipedia, the free encyclopedia
A Course of Mathematics for the use of the Royal Military Academy, by Charles Hutton. ... A Course of Mathematics, by C. Hutton, continued by O. Gregory; ...
en.wikipedia.org/ wiki/ Thomas_Stephens_Davies

Geometry.Net - Scientists: Hutton Charles
Composed for the use of the Royal military academy by Charles Hutton, 1841; A course of mathematics: In two volumes. For the use of academies, ...
www.geometry.net/ scientists/ hutton_charles_page_no_4.php

Collection of Early American Mathematics Books
Main Title TM: A course of mathematics : in two volumes : for the use of academies, as well as private tuition / by Charles Hutton. ...
www.math.gatech.edu/ ~hill/ publications/ books/ booklist.html

Amy Ackerberg-Hastings
In the mathematics part of the course, Mansfield taught algebra and Barron covered geometry, both from Charles Hutton's A Course of Mathematics. ...
www.math.usma.edu/ people/ Rickey/ dms/ DeptHeads/ Davies%20by%20Amy%20Ackerberg-Hastings.rtf

SOURCES - page 1. BIOGRAPHICAL MATERIAL -- in chronological order ...
SOURCES - page. 1. BIOGRAPHICAL MATERIAL -- in chronological order. ALCUIN (c735-804). Phillip Drennon Thomas. Alcuin of York. DSB I, 104-105. ...
www.g4g4.com/ MyCD5/ SOURCES/ SOURCE2.DOC

JSTOR: Muskets and Pendulums: Benjamin Robins, Leonhard Euler, and ...
Never- theless, the mathematics taught by Hutton, as demonstrated by his textbook A Course of Mathematics, in Two Volumes: Composed and more Especially ...