Elements of geometry: consisting of the first four,and the sixth, books of Euclid, with the principal theorems in proportion [&c.] by J. Narrien1842 |
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Σελίδα
... numbers ; their greatest common measures and least common multiples ; continued and mean proportionals . The tenth book relates to incommensurable quantities . The eleventh The and twelfth books treat of the intersections of planes ,
... numbers ; their greatest common measures and least common multiples ; continued and mean proportionals . The tenth book relates to incommensurable quantities . The eleventh The and twelfth books treat of the intersections of planes ,
Σελίδα 106
... measured by the less , that is , when the greater contains the less a certain number of times exactly . III . A less magnitude , or number , is said to be a part , or a sub- multiple , of a greater magnitude , or ... measure ELEMENTS ...
... measured by the less , that is , when the greater contains the less a certain number of times exactly . III . A less magnitude , or number , is said to be a part , or a sub- multiple , of a greater magnitude , or ... measure ELEMENTS ...
Σελίδα 107
Euclides John Narrien. VI . Magnitudes are incommensurable which have no common measure . VII . Ratio is the relation which one magnitude has to another of the same kind , with respect to quantity ; or when the first is considered as ...
Euclides John Narrien. VI . Magnitudes are incommensurable which have no common measure . VII . Ratio is the relation which one magnitude has to another of the same kind , with respect to quantity ; or when the first is considered as ...
Σελίδα 109
... measures two other magnitudes , will likewise measure both their sum and their difference . II . In any proportion among magnitudes , the first and third terms remaining the same , if the second be increased or diminished by any ...
... measures two other magnitudes , will likewise measure both their sum and their difference . II . In any proportion among magnitudes , the first and third terms remaining the same , if the second be increased or diminished by any ...
Σελίδα 112
... measure them both . And because м measures B , it will measure its mul- tiple , which is contained in A ; but it likewise measures A ; wherefore it will measure C , the difference between A and the multiple of B ( 1. Axiom , Proportion ) ...
... measure them both . And because м measures B , it will measure its mul- tiple , which is contained in A ; but it likewise measures A ; wherefore it will measure C , the difference between A and the multiple of B ( 1. Axiom , Proportion ) ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Elements of Geometry: Consisting of the First Four,and the Sixth, Books of ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal adjacent angles altitudes angle ABC angle ACB angle BAC assigned base BC bisected centre circle ABC circumference cone convex surface cylinder described diameter draw drawn duplicate ratio Edition equal angles equal or equivalent equi equilateral and equiangular Euclid exterior angle fore given line given rectilineal given straight line gnomon greater Greek homologous homologous sides inscribed join Latin Let ABC measure number of sides opposite angles parallel parallelepiped parallelogram perpendicular picket plane angles prism PROB proportional proposition pyramid Q. E. D. PROP rectangle contained rectilineal figure regular polygon remaining angle right angles segment similar solid angle sphere spherical angle square of AC straight line AC THEOR touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 55 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Σελίδα 47 - CB ; wherefore the four figures HF, CK, AG, GE are equal to the squares of AC, CB, and to twice the rectangle AC, CB : but HF, CK, AG, GE make up the whole figure ADEB, which is the square of AB: therefore the square of AB is equal to the squares of AC, CB, and twice the rectangle AC, CB. Wherefore, if a straight line, &c.
Σελίδα 12 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity...
Σελίδα 73 - CBED is greater than a semicircle, the angles CAD, CED are equal : therefore the whole angle BAD is, equal to the whole angle BED.
Σελίδα 8 - A New Treatise on the Use of the Globes ; or, a Philosophical View of the Earth and Heavens : comprehending an Account of the Figure, Magnitude, and Motion of the Earth: with the Natural Changes of its Surface, caused by Floods, Earthquakes, &c.
Σελίδα 142 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 11 - ABC is therefore equal to the remaining angle ACB, which are the angles at the base of the triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB, which are the angles upon the other side of the base. Therefore, " the angles at the base
Σελίδα 53 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 30 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Σελίδα 9 - If two triangles have two sides of the one equal to two sides of the...