The mechanical Euclid, containing the elements of mechanics and hydrostatics1837 |
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Σελίδα 16
... triangle be given the base varies as the perpendicular altitude . If A , a represent the altitudes , B , b the bases of two triangles , since a triangle is half the rectangle on the same base and of the same altitude , and the tri- angles ...
... triangle be given the base varies as the perpendicular altitude . If A , a represent the altitudes , B , b the bases of two triangles , since a triangle is half the rectangle on the same base and of the same altitude , and the tri- angles ...
Σελίδα 23
... triangle into two equal angles . * PROP . IV . The sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are homologous sides ; that is , are the antecedents or ...
... triangle into two equal angles . * PROP . IV . The sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are homologous sides ; that is , are the antecedents or ...
Σελίδα 47
... angle qCA is equal to the alternate angle DrA . the triangles CAq , DAr are equiangular . and Dr are equal , for each is equal to opposite sides of parallelograms pq , pr . ( Euc . vI . 8 ) the other sides of the triangles CAq , DAr are ...
... angle qCA is equal to the alternate angle DrA . the triangles CAq , DAr are equiangular . and Dr are equal , for each is equal to opposite sides of parallelograms pq , pr . ( Euc . vI . 8 ) the other sides of the triangles CAq , DAr are ...
Σελίδα 78
William Whewell. Also , if AH be not an exact multiple of AF , or AN of AM , we may , in the reasoning , neglect the last particle in Ab , and Ae , and the ... triangles have two angles of the one equal to two angles 78 MECHANICS .
William Whewell. Also , if AH be not an exact multiple of AF , or AN of AM , we may , in the reasoning , neglect the last particle in Ab , and Ae , and the ... triangles have two angles of the one equal to two angles 78 MECHANICS .
Σελίδα 79
William Whewell. have two angles of the one equal to two angles of the other ; and the side KL is equal to LM . Therefore the triangles are equal , and HL is equal to MN ; that is , to RS . In the same manner it may be shewn that OQ is ...
William Whewell. have two angles of the one equal to two angles of the other ; and the side KL is equal to LM . Therefore the triangles are equal , and HL is equal to MN ; that is , to RS . In the same manner it may be shewn that OQ is ...
Άλλες εκδόσεις - Προβολή όλων
The Mechanical Euclid, Containing the Elements of Mechanics and Hydrostatics William Whewell Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
acting added angles appears arising axioms balance base body BOOK called center of gravity column common considered containing definition described destroy difference direction divided draw drawn effect equal equilibrium exerted expressed facts falling fixed fluid force forces acting fraction fulcrum Geometry given greater heavy Hence HISTORY horizontal idea increase Inductive less lever magnitude manner mathematical matter means Mechanics motion move multiplied nature opposite parallel particles pass perpendicular plane portions position pressure principles prism produce Prop proportion proposition proved quantity ratio reasoning reference represented respectively rest rigid round sides space specific gravity straight line string supported supposed surface taken tions triangle truth tube turn uniform upwards velocity vertical weight whole
Δημοφιλή αποσπάσματα
Σελίδα 22 - A plane is perpendicular to a plane, when the straight lines drawn in one of the planes perpendicular to the common section of the two planes, are perpendicular to the other plane. 5. The inclination of a straight line to a plane...
Σελίδα 46 - If three forces, represented in magnitude and direction by the sides of a triangle, act on a point, they will keep it at rest.
Σελίδα 9 - Sacred History, from the Creation of the World to the Destruction of Jerusalem. With Questions for Examination.
Σελίδα 18 - ... if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth : or, if the multiple of the first be greater than that of the second, the multiple of the third is also greater than that of the fourth.
Σελίδα 47 - There is an equilibrium upon the wheel and axle when the power is to the weight as the radius of the axle to the radius of the wheel.
Σελίδα 20 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Σελίδα 97 - ... gravity of the fluid : the specific gravity of the body. Prop. 10. To describe the hydrostatic balance, and to shew how to find the specific gravity of a body by means of it, 1st, when its specific gravity is greater than that of the fluid in which it is weighed ; 2ndly, when it is less.