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 x
... multiple Points , of Points of Inflec- tion , Points of contrary Inflection , of Serpentment , & c . Thefe Theo- ries are founded partly upon the fimple algebraic Calculation , and partly on the direct Method of Fluxions . Then they are ...
... multiple Points , of Points of Inflec- tion , Points of contrary Inflection , of Serpentment , & c . Thefe Theo- ries are founded partly upon the fimple algebraic Calculation , and partly on the direct Method of Fluxions . Then they are ...
Page 160
... multiples of each other , or aliquot parts , or aliquant parts . For if the quantities M and N , are commenfurable , N ... multiple of N , in the fecond cafe M , is an aliquot part of N , and in the third , the leffer of the two is an ...
... multiples of each other , or aliquot parts , or aliquant parts . For if the quantities M and N , are commenfurable , N ... multiple of N , in the fecond cafe M , is an aliquot part of N , and in the third , the leffer of the two is an ...
Page 161
... multiple of a lefs , when the greater is measured by the less . Thus , the number 12 is faid to be a multiple , of the number 4 , becaufe 4 mea- fures 12 without a remainder . To the term of multiple corresponds that of submultiple ...
... multiple of a lefs , when the greater is measured by the less . Thus , the number 12 is faid to be a multiple , of the number 4 , becaufe 4 mea- fures 12 without a remainder . To the term of multiple corresponds that of submultiple ...
Page 162
... the fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatfoever of the fecond and fourth . DEFINITIONS . If the multiple of the first , be 162 Book V. The ELEMENTS.
... the fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatfoever of the fecond and fourth . DEFINITIONS . If the multiple of the first , be 162 Book V. The ELEMENTS.
Page 163
... multiple of the third is alfo less than that of the fourth ; or if the multiple of the first be equal to that of the fecond , the multiple of the third is alfo equal to that of the fourth , or if the multiple of the first be greater ...
... multiple of the third is alfo less than that of the fourth ; or if the multiple of the first be equal to that of the fecond , the multiple of the third is alfo equal to that of the fourth , or if the multiple of the first be greater ...
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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...