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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Page xi
... Preparation ; the Methods for knowing and diftinguishing these Quantities or Equations ; afterwards they pafs to the Methods of finding the Fluents of fluxional Quantities , which have fecond Part need of being prepared by fome ...
... Preparation ; the Methods for knowing and diftinguishing these Quantities or Equations ; afterwards they pafs to the Methods of finding the Fluents of fluxional Quantities , which have fecond Part need of being prepared by fome ...
Page 16
... Preparation . Thefis . 1. BC EF . = II . Vb Ye & Vc = Vf . = III . A BAC = △ EDF . Suppose the ABAC to be laid upon the △ EDF , in fuch a man- ner that 1. The point A falls upon the point D. 2. And the fide AB falls upon the fide DE ...
... Preparation . Thefis . 1. BC EF . = II . Vb Ye & Vc = Vf . = III . A BAC = △ EDF . Suppose the ABAC to be laid upon the △ EDF , in fuch a man- ner that 1. The point A falls upon the point D. 2. And the fide AB falls upon the fide DE ...
Page 20
... . Fig . 2 . Preparation . 1. From the point D to the point C , draw the ftraight line DC . Pof . I. 2. Produce at will BD to E & BC to F. Pof . 2 . BECAUSE ECAUSE AC is fuppofed AD . 1. The ACAD 20 Book I. The ELEMENTS.
... . Fig . 2 . Preparation . 1. From the point D to the point C , draw the ftraight line DC . Pof . I. 2. Produce at will BD to E & BC to F. Pof . 2 . BECAUSE ECAUSE AC is fuppofed AD . 1. The ACAD 20 Book I. The ELEMENTS.
Page 21
... Preparation . From the point D to the point C let there be drawn the straight line DC . BECAUSE ECAUSE AC is fuppofed AD . 1. The A CAD will be an ifofceles A. 2. Confequently Vb & d + c at the bafe are equal to one another . Again ...
... Preparation . From the point D to the point C let there be drawn the straight line DC . BECAUSE ECAUSE AC is fuppofed AD . 1. The A CAD will be an ifofceles A. 2. Confequently Vb & d + c at the bafe are equal to one another . Again ...
Page 22
... Preparation . Let the AFHG be applied to the △ ACB , so that , 1. The point F may coincide with the point A. 2. And the bafe FG with the bafe AB . DEMONSTRATION . BECAUSE the point F coincides with the point A ( Prep . 1. ) , & the ...
... Preparation . Let the AFHG be applied to the △ ACB , so that , 1. The point F may coincide with the point A. 2. And the bafe FG with the bafe AB . DEMONSTRATION . BECAUSE the point F coincides with the point A ( Prep . 1. ) , & the ...
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Common terms and phrases
ABCD alfo alſo arch bafe baſe becauſe Bodies Cafe caufe centrifugal Force circle Cofine Comet cone Confequently cylinder defcribed demonftrated Diameter diſcovered Diſtance draw the ftraight Earth ECAUSE Ecliptic equal Equator equiangular equimultiples fame altitude fame manner fame multiple fame plane fame ratio fecond fegment fhall fhewing fhould fide AC fimilar fince firft firſt folid fome Force fquare ftraight lines AC fuch fuppofed Gravity greateſt heliocentric Hypothefis impoffible interfect Jupiter lefs Likewife line A B magnitude Meaſure Moon moſt Motion Newton Nodes Number Obfervations oppofite Orbit pafs thro parallelepiped Perihelion plle Prep prifm proportional PROPOSITION pyramid Rays rectilineal figure Revolution Rgle right angles Saturn ſphere Syfigies Syftem Tangent thefe Thefis THEOREM theſe thofe thoſe Tides tion triangle true Anomaly Vafe Wherefore whofe
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 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 8 - 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 164 - 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 29 - 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 29 - 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...