## Instructions Given in the Drawing School Established by the Dublin Society: Course of mathematicks. System of the physical world. System of the moral world. Plan of the military art. Plan of the marcantile arts. Plan of naval art. Plan of mechanic arts. The elements of EuclidA. M'Culloch, 1769 - Mathematics |

### From inside the book

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**Prep**. 1. ) , & the line AB upon the line DE (**Prep**. 2. ) . 1. The point B will fall necessarily upon the point E. Because the Va = d ( Hyp . 3. ) , & the point A falls upon the point D (**Prep**. 1. ) , & the side AB upon the side DE (**Prep**... Page 17

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**Prep**. 2 , Arg . 2. ) . 7. Those two ABAC , EDF , are necessarily equal to one another . Which was to be demonstrated . III . In fine , since the b & Ve to which the equal fides AC , DF are op- posite ( Hyp . 2. ) ; likewise , the Vc ... Page 18

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**Prep**. 2. Hyp . 1. ) ; and the A contained by those equal fides is common to the two Δ . 1. The bafe DC is = to the base BE ; & the two remaining ∀m & b + d of A DAC , are equal to the two remaining ∀n & a + c of EAB , each to each of ... Page 19

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**Prep**. 1. ) , the fide BC is common to the two tained b + c ( Hyp . 1. ) . 1. Consequently , the two & contained a = ∀ con- DBC , have two sides of the one equal to two fides of the other , cach to each , & ∀ ontained a = V con ... Page 22

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**Prep**. 1. ) , & the line FG with the line AB (**Prep**. 2. ) , & those lines are equal ( Hyp . 3. ) . 1. The point G must coincide with the point B. The extreme points F & G of the side FG , coinciding therefore with the extreme points A ...### Other editions - View all

### Common terms and phrases

ABCD alfo alſo altitude arch Axis bafe baſe becauſe Bodies Cauſe chords circle Comet cone Conſequently cylinder demonſtrated DEMONSTRATION deſcribe diameter Diſtance draw the ſtraight Earth ECAUSE Ecliptic equal Equator equiangular equimultiples fame manner fame multiple fides AC fimilar fince firſt folid Force given Glaſs Gravity Hypothefis impoſſible interfect inverſe Jupiter leaſt leſs Likewife magnitude Meridian Moon moſt Motion neceſſary Newton Nodes Number Obſervations oppoſite Orbit parallelepiped parallelogram paſs paſſes thro Perihelion plane plle Poſition Prep priſm produced proportional PROPOSITION pyramid Quadratures ratio Rays rectilineal figure reſpect Rgle right angles ſame Saturn ſecond ſegment ſenſible ſerve ſhall ſhewing ſhewn ſhould ſide ſmall ſphere ſquare ſuch ſuppoſed Syſtem Tangent THEOREM theſe Theſis thoſe Tides tion triangle true Anomaly Wherefore whoſe

### Popular passages

Page 8 - Let it be granted that a straight line may be drawn from any one point to any other point.

Page 4 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Page 164 - When of the equimultiples of four magnitudes (taken as in the fifth definition), the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth : and, on the contrary, the third is said to have to the fourth a less ratio than the first has to the second. VIII. " Analogy, or proportion, is the similitude of ratios.

Page 165 - When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c., increasing the denomination still by unity, in any number of proportionals.

Page 241 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, etc.

Page xxviii - ... bodies that are within the sphere of their activity, and consequently, that not only the sun and moon have .an influence upon the body and motion of the earth, and the earth upon them, but that...

Page 165 - When three magnitudes are proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second.

Page 226 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Page xiv - Oh! qui m'arrêtera sous vos sombres asiles? Quand pourront les neuf Sœurs, loin des cours et des villes, M'occuper tout entier, et m'apprendre des deux Les divers mouvements inconnus à nos yeux, Les noms et les vertus de ces clartés errantes Par qui sont nos destins et nos mœurs différentes.

Page xxviii - Now what these several degrees are I have not yet experimentally verified; but it is a notion which, if fully prosecuted, as it ought to be, will mightily assist the astronomers to reduce all the celestial motions to a certain rule, which I doubt will never be done true without it.