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
... follow the sixth , have been omitted or only partially followed ; and it will be proper here to state the reason for adopting a method different from that of Euclid , in treating the subject of proportion among geometrical mag- nitudes ...
... follow the sixth , have been omitted or only partially followed ; and it will be proper here to state the reason for adopting a method different from that of Euclid , in treating the subject of proportion among geometrical mag- nitudes ...
Σελίδα
... follow that x is greater than that multiple of B ; but the altitudes of A and B being equal , and the base of x being less than that of a or B , x is less than that multiple of B ( because it is equal to the same multiple of a pyramid ...
... follow that x is greater than that multiple of B ; but the altitudes of A and B being equal , and the base of x being less than that of a or B , x is less than that multiple of B ( because it is equal to the same multiple of a pyramid ...
Σελίδα
... follow , from equality of ratios , and because x is greater than the figure inscribed in it , that M is greater than s : but , as above , it is less , which is impossible ; therefore a is not to B as X is to a magnitude less than Y. On ...
... follow , from equality of ratios , and because x is greater than the figure inscribed in it , that M is greater than s : but , as above , it is less , which is impossible ; therefore a is not to B as X is to a magnitude less than Y. On ...
Σελίδα
... follow that the method employed in this work is in accordance with the spirit of the ancient geometry . Now it is a necessary corollary from the first proposition of Euclid's tenth book , that by continual bisections of the ...
... follow that the method employed in this work is in accordance with the spirit of the ancient geometry . Now it is a necessary corollary from the first proposition of Euclid's tenth book , that by continual bisections of the ...
Σελίδα 13
... follows that all the angles of the one triangle are equal to all the angles of the other , each to each , as in the conclusion of that proposition . Also that the two triangles are equal to one another in every respect . PROP . IX ...
... follows that all the angles of the one triangle are equal to all the angles of the other , each to each , as in the conclusion of that proposition . Also that the two triangles are equal to one another in every respect . PROP . IX ...
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...