An essay on mechanical geometry, explanatory of a set of models1796 |
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Página 13
... halves of the same , are equal to one another . 8 . Magnitudes which coincide with one another , that is , which exactly fill the fame fpace , are equal to one another . 9 . 9 . The whole is greater than its part . Axioms . 13 Book 1 .
... halves of the same , are equal to one another . 8 . Magnitudes which coincide with one another , that is , which exactly fill the fame fpace , are equal to one another . 9 . 9 . The whole is greater than its part . Axioms . 13 Book 1 .
Página 20
... coincide with the angle FGD ; but this will be fufficiently clear without cutting the figure . For the angle AFG is equal to the angle EFB by Theorem the 5th ; and the angle FGD is alfo equal to the angle EFB by Theorem 6th ; therefore ...
... coincide with the angle FGD ; but this will be fufficiently clear without cutting the figure . For the angle AFG is equal to the angle EFB by Theorem the 5th ; and the angle FGD is alfo equal to the angle EFB by Theorem 6th ; therefore ...
Página 21
... coincide and cover the triangle BAC , and therefore must be equal in every respect . THEOREM 9. The angles at the base of an ifofceles triangle are equal . Thus the tri- angle ABC having the two sides AC and BC C.13 equal , the angle A ...
... coincide and cover the triangle BAC , and therefore must be equal in every respect . THEOREM 9. The angles at the base of an ifofceles triangle are equal . Thus the tri- angle ABC having the two sides AC and BC C.13 equal , the angle A ...
Página 22
... coincide with , or cover it ; therefore the angles A and B are equal . Corollary . If the angle C of an isofcles triangle be bifected , the bifecting line will be perpendicular to the Bafe , viz . CD per- pendicular to AB . THEOREM 10 ...
... coincide with , or cover it ; therefore the angles A and B are equal . Corollary . If the angle C of an isofcles triangle be bifected , the bifecting line will be perpendicular to the Bafe , viz . CD per- pendicular to AB . THEOREM 10 ...
Página 26
... coincide with AB ; the point F will fall on the point C , and the triangles exactly coincide ; therefore are they equal in every respect . THEOREM THEOREM 17. Similar triangles have their like sides proportional ; 26 Theorems . Book I.
... coincide with AB ; the point F will fall on the point C , and the triangles exactly coincide ; therefore are they equal in every respect . THEOREM THEOREM 17. Similar triangles have their like sides proportional ; 26 Theorems . Book I.
Otras ediciones - Ver todas
An Essay on Mechanical Geometry, Explanatory of a Set of Models Benjamin Donne Sin vista previa disponible - 2019 |
An Essay on Mechanical Geometry, Explanatory of a Set of Models Benjamin Donne Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 11 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Página 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...
Página 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.
Página 12 - ... the three angles of a triangle are together equal to two right angles, although it is not known to all.
Página 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.
Página 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.
Página 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.
Página 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...
Página 40 - SIMILAR cones and cylinders have to one another the triplicate ratio of that which the diameters of their bases have...