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 110
... ( ABCD , AGDF or ABCD , BECH , ) which touch each other ; whether internally ; or externally : cannot touch in more points than one . Hypothefis . 1.O ABCD touches O AGDF internally . II . O ABCD touches O BECH externally . * If not , 1 ...
... ( ABCD , AGDF or ABCD , BECH , ) which touch each other ; whether internally ; or externally : cannot touch in more points than one . Hypothefis . 1.O ABCD touches O AGDF internally . II . O ABCD touches O BECH externally . * If not , 1 ...
Page 124
... ABCD being to the two fides HE , HG , of the A EHG ( Hyp . 3. & Ax . 1. B. 3. ) , & the VC = to the VH ( Hyp . 2. ) . 1. The base BD will be to the bafe EG . And because VA is = P. 4. B. 1 . to VF ( Hyp . 1. ) . Ax . 2. B.3 . to the ...
... ABCD being to the two fides HE , HG , of the A EHG ( Hyp . 3. & Ax . 1. B. 3. ) , & the VC = to the VH ( Hyp . 2. ) . 1. The base BD will be to the bafe EG . And because VA is = P. 4. B. 1 . to VF ( Hyp . 1. ) . Ax . 2. B.3 . to the ...
Page 139
... ( ABCD ) ; when all the fides ( EF , FG , GH , HE ) of the circumfcribed figure pass thro ' the angular points ( A , B , C , D ) of the figure about which it is defcribed , each thro ' each ( Fig . 1 ) . IIL A rectilineal figure ( ABCD ) ...
... ( ABCD ) ; when all the fides ( EF , FG , GH , HE ) of the circumfcribed figure pass thro ' the angular points ( A , B , C , D ) of the figure about which it is defcribed , each thro ' each ( Fig . 1 ) . IIL A rectilineal figure ( ABCD ) ...
Page 140
... ( ABCD ) is faid to be inferibed in a rectilineal figure ( EFGH ) , when the circumference of the circle touches each of the fides ( EF , FG , GH , HE ) of the figure in which it is infcribed ( Fig . 1 ) . VI . A circle ( ABCD ) is ...
... ( ABCD ) is faid to be inferibed in a rectilineal figure ( EFGH ) , when the circumference of the circle touches each of the fides ( EF , FG , GH , HE ) of the figure in which it is infcribed ( Fig . 1 ) . VI . A circle ( ABCD ) is ...
Page 147
... ( ABCD ) about a given Circle ( HEFI ) . Given . The HEFI . Sought . The ABCD defcribed about the HEFI . Refolution . 5 . 1. Draw the diameters EI , HF fo as to cut each other at L. 2. At the Extremities H , E , F , I of thofe diameters ...
... ( ABCD ) about a given Circle ( HEFI ) . Given . The HEFI . Sought . The ABCD defcribed about the HEFI . Refolution . 5 . 1. Draw the diameters EI , HF fo as to cut each other at L. 2. At the Extremities H , E , F , I of thofe diameters ...
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Common terms and phrases
ABCD alfo alſo arch bafe baſe becauſe Bodies Cafe circle Cofine Comet cone Confequently cylinder defcribed demonftrated DEMONSTRATION diameter difcovered 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 fimilar fince firft firſt folid fome Force fphere fquare ftraight lines AC fuch fuppofed given Gravity greateſt heliocentric Hypothefis impoffible interfect Jupiter leaft lefs Likewife line A B magnitude Meaſure Moon moſt Motion Newton Nodes Number Obfervations oppofite Orbit paffes pafs parallelepiped parallelogram Perihelion plle Prep prifm proportional PROPOSITION pyramid Rays rectilineal figure Revolution Rgle right angles Saturn Syfigies Syftem Tangent thefe Thefis THEOREM theſe thofe thoſe thro Tides tion triangle true Anomaly Vafe Wherefore whofe
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.