An essay on mechanical geometry, explanatory of a set of models1796 |
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Page 28
... fquare , agreeable to their num- bers ; and they cover the yellow fquare . In like manner lay the three cut parts stained green on the refpective parts of the square coloured green , and they will exactly cover that fquare . Now to ...
... fquare , agreeable to their num- bers ; and they cover the yellow fquare . In like manner lay the three cut parts stained green on the refpective parts of the square coloured green , and they will exactly cover that fquare . Now to ...
Page 32
... fquare of the line is equal to 4 times the fquare on half that line . Corollary I of D. I. Let AC reprefent a line ; AB its half ; then it is manifeft by a bare inspection of the figure , that the fquare on the whole line AC , viz ...
... fquare of the line is equal to 4 times the fquare on half that line . Corollary I of D. I. Let AC reprefent a line ; AB its half ; then it is manifeft by a bare inspection of the figure , that the fquare on the whole line AC , viz ...
Page 33
... fquare of the whole line is equal to the Squares on the two parts , and twice the rectangle contained by the parts AC , CB . - 4 E. 2 , or 2 D. 2 . For by inspection of the figure , the fquare C.25 ABDE is the fquare on the whole line ...
... fquare of the whole line is equal to the Squares on the two parts , and twice the rectangle contained by the parts AC , CB . - 4 E. 2 , or 2 D. 2 . For by inspection of the figure , the fquare C.25 ABDE is the fquare on the whole line ...
Page 36
... fquare be twice as long as the fide of the leffer fquare ; then , by a bare inspection , it appears that the large square contains four of the finall squares . If AB C.29 is equal to 1 inch , the leffer fquare contains a space of 1 ...
... fquare be twice as long as the fide of the leffer fquare ; then , by a bare inspection , it appears that the large square contains four of the finall squares . If AB C.29 is equal to 1 inch , the leffer fquare contains a space of 1 ...
Page 37
... fquare were 3 , it would contain 3 multiplied by 3 , equal to 9 times the furface , or area of the leffer fquare . Hence two fquares are to one an- other as the fquares of their fides . އ If a triangle were to be infcribed in each of ...
... fquare were 3 , it would contain 3 multiplied by 3 , equal to 9 times the furface , or area of the leffer fquare . Hence two fquares are to one an- other as the fquares of their fides . އ If a triangle were to be infcribed in each of ...
Other editions - View all
An Essay on Mechanical Geometry, Explanatory of a Set of Models Benjamin Donne No preview available - 2019 |
An Essay on Mechanical Geometry, Explanatory of a Set of Models Benjamin Donne No preview available - 2016 |
Common terms and phrases
180 degrees alfo alſo Analemma angle ACD arithmetic arithmetical mean bafe baſe bifect Book breadth Briſtol called circle circumfcribing compaffes conceived cone confequently contained Corollary croffing cylinder demonftrations deſcribe diameter diſtance divided effay Euclid exactly expreffed faid fame number femicircle fhall fhewn fhould fides fignifies figure fimilar fmall folid fome four numbers fquare feet fruftum ftands ftraight fubtract fufficiently furface gallons geometrical mean Geometricians Geometry globe height Hence inftance interfect large cube length manifeft meaſure multiply half muſt number of degrees number of feet numbers are proportional oppofite orem parallel lines parallel ruler parallelogram perpendicular planes pofition pole prefent priſm PROBLEM propofitions purpoſe pyramid radius reaſon rectangle regular polygon repreſent reſpect rhombus right angles right line ſcheme Scholium ſet ſhadow ſhall ſquare Theorem theſe Thomas Beddoes thoſe three angles triangle ABC whole yards
Popular passages
Page 4 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Page 11 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Page 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 24 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 12 - ... the three angles of a triangle are together equal to two right angles, although it is not known to all.
Page 37 - A right circular cone is often called a cone of revolution, because it can be generated by the revolution of a right-angled triangle about one of its shorter sides.
Page 10 - POSTULATES. 1. LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Page 65 - Multiply half the circumference by half the diameter, and the product will be the area. Or, divide the product of the whole circumference and diameter -by 4, and the quotient will be the area. 2. Multiply the square of the diameter by .7854, and the product will be the area.
Page 84 - ... reafonable creatures •, for though we all call ourfelves fo, becaufe we are born to it if we pleafe, yet we may truly fay Nature gives us but the...
Page 40 - SIMILAR cones and cylinders have to one another the triplicate ratio of that which the diameters of their bases have...