## 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 |

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

### Popular passages

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 162 - 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 163 - 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 6 - Let it be granted that a straight line may be drawn from any one point to any other point.

Page xxviii - This depends upon three suppositions: — first, that all celestial bodies whatsoever have an attraction or gravitating power towards their own centres, whereby they attract not only their own parts and keep them from flying from them, as we may observe the earth to do, but that they do also attract all the other celestial bodies that are within the sphere of their activity...

Page 162 - VII. 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...

Page 27 - Therefore if two straight lines, &c. QED COR. 1. From this it is manifest, that, if two straight lines cut one another, the angles they make at the point where they cut, are together equal to four right angles.

Page 27 - Cor. 2. And consequently that all the angles made by any number of lines meeting in one point, are together equal to four right angles.

Page xxviii - Saturn also, by their attractive powers, have a considerable influence upon its motion, as in the same manner the corresponding attractive power of the earth hath a considerable influence upon every one of their motions also.

Page xxviii - The third supposition is that these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own centers. Now what these several degrees are I have not yet experimentally verified...