## 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 Euclid |

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Resultat 1-5 av 5

Side 83

PROPOSITION IX . THEOREM IX . Fa ftraight linc ( AB ) be divided into two equal

parts ( AC , CB , ) , & into two unequal parts ( AD , DP , ) ; the squares of the two

urequal parts ( AD , DB ) are together double of the the square of the

...

PROPOSITION IX . THEOREM IX . Fa ftraight linc ( AB ) be divided into two equal

parts ( AC , CB , ) , & into two unequal parts ( AD , DP , ) ; the squares of the two

urequal parts ( AD , DB ) are together double of the the square of the

**half**( AC ) of...

Side 85

Hence each of the V CAE & mis

manner that : 3. Each of the Vp & n is

to L. Ax . 2. B. r . Moreover , Vp being

Hence each of the V CAE & mis

**half**a L P. 32. B. 1 . It is proved in the famemanner that : 3. Each of the Vp & n is

**half**a Le . 4. Consequently , Vmt n will be =to L. Ax . 2. B. r . Moreover , Vp being

**half**a L ( Arg . 3. ) . 5. The Vo will be also**half**a ... Side 304

G L E M M A. If from the greater ( A B ) , of two unequal magnitudes ( A B & C ) ,

there be taken more than its

than its

G L E M M A. If from the greater ( A B ) , of two unequal magnitudes ( A B & C ) ,

there be taken more than its

**half**( viz . A H ) , and from the remainder ( H B ) morethan its

**half**( viz . H K ) , and so on : there shall at length remain a magnitude ... Side 306

The

ILNP is = to

diameter , & the of the diameter = OLIOLN = 2 OLI ) . P.47 . B. 1 . 2. Therefore , the

...

The

**half**of this will be > the**half**of the O IL P. P.19 . B. 5 . But the inscribed OILNP is = to

**half**of the circumscribed 0 ( the side of the circumscribed being to thediameter , & the of the diameter = OLIOLN = 2 OLI ) . P.47 . B. 1 . 2. Therefore , the

...

Side 322

Therefore , the EP upon BDCA is the

since the ATAC is the

described upon this ATAC , will be the ( P.28 . B.11 .

K. P.34 .

Therefore , the EP upon BDCA is the

**half**of the same cylinder . P.19 . B. 5 . Andsince the ATAC is the

**half**of the pgr . A K. P.41 . B. i . 4. The prism ETF ,described upon this ATAC , will be the ( P.28 . B.11 .

**half**of the Eupon the pgr . AK. P.34 .

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Instructions Given in the Drawing School Established by the Dublin Society ... Joseph Fenn Uten tilgangsbegrensning - 1769 |

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added alſo altitude angles arch Attraction baſe becauſe Bodies circle Comet common cone Conſequently contained cylinder demonſtrated deſcribed determined Diameter diſcovered Diſtance divided double draw drawn Earth ECAUSE equal Equator Eſq Experiments fall fame fides figure firſt follows Force given Gravity greater half Height Hypotheſis Jupiter Laws leſs Likewiſe magnitude manner mean meet Moon Motion multiple Nature Newton Nodes Number Obſervations oppoſite Orbit paſſes Place plane plle Prep Preparation priſm produced proportional PROPOSITION proved pyramid Quantity ratio Rays remaining revolve Rgle round ſame Saturn ſecond ſhould ſides ſimilar ſince ſphere ſtraight line ſuppoſed taken THEOREM theſe Theſis third thoſe thro Tides tion triangle Waters Wherefore whole whoſe

### Populære avsnitt

Side 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.

Side 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.

Side 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.

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

Side 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...

Side 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...

Side 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.

Side 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.

Side 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.

Side 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...