## 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 |

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Página 30

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**interfect**each other at the point D. ( Prep . 2. ) . P. 10. B. I. Pof . 1 . P. 3. B. 1 . Pof . 1 . 1. Confequently , the oppofite vertical VCDA , BDE , are to one another . P. 15. B. 1 . Wherefore fince in the △ ACD , DEB , the fide CD ... Página 77

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**interfect**each other in a point E of the diagonal , the Rgles BF , DH , formed about the diagonal , are fquares . IF COROLLARY II . F the line AC be divided into two equal parts in B , the complements AE , EI , are fquares , & thofe ... Página 148

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**interfect**each other , at the distance CA defcribe the BECAUSE ABDE . DEMONSTRATION . ECAUSE the figures FE , BH , FD , AH , FC , AE , BD , CH are But the whole lines FI , FG being equal ( D. 30. B. 1. ) and FA , FB being the halves of ... Página 149

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**interfect**each other , and at the distance CA , describe the ABDE . DEMONSTRATION . BECAUSE in A ABE , EBD the fide AB is to the fide BD AE to ED ( D. 30. B. 1. ) , & BE common to the two A. 1. The ABE is to Y EBD , & the whole by BE ... Página 155

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**interfect**each other , at the distance CA describe the O ADF . Preparation . Pof . 3 . Pof . 1 . 5 . Draw the straight lines CB , CD , CE . THE DEMONSTRATION . HE ftraight lines CB , CD , CE bifect the V ABD , BDE , DEF . ( P. 13. B. 4 ...### Otras ediciones - Ver todas

### Términos y frases comunes

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

### Pasajes populares

Página 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.

Página 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.

Página 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.

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

Página 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...

Página 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...

Página 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.

Página 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.

Página 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.

Página 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...