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 8
... equal ( 15. Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to BA : but it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB : but things which are equal ...
... equal ( 15. Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to BA : but it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB : but things which are equal ...
Σελίδα 9
... equal to DG , and DA , DB , parts of them are equal ( 1. 1. ) : therefore the remainder AL is equal to the remainder ( 3 Ax . ) BG : But it has been shown , that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and ...
... equal to DG , and DA , DB , parts of them are equal ( 1. 1. ) : therefore the remainder AL is equal to the remainder ( 3 Ax . ) BG : But it has been shown , that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and ...
Σελίδα 10
... equal to the angle EDF ; the base BC shall be equal to the base EF ; and the tri- angle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite shall be equal , each to each , viz . the angle Да B ABC to the ...
... equal to the angle EDF ; the base BC shall be equal to the base EF ; and the tri- angle ABC to the triangle DEF ; and the other angles to which the equal sides are opposite shall be equal , each to each , viz . the angle Да B ABC to the ...
Σελίδα 11
... equal ( 4.1 . ) to the remaining angles of the other , each to each , to which the equal sides are opposite , viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB : And because the whole AF is equal to the whole AG ...
... equal ( 4.1 . ) to the remaining angles of the other , each to each , to which the equal sides are opposite , viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB : And because the whole AF is equal to the whole AG ...
Σελίδα 12
Euclides John Narrien. DBC is equal ( 4. 1. ) to the triangle ACB , the less to the greater ; which is absurd . Therefore A B is not unequal to AC , that is , it is equal to it . Wherefore , if two angles , & c . Q. E. D. COR . Hence ...
Euclides John Narrien. DBC is equal ( 4. 1. ) to the triangle ACB , the less to the greater ; which is absurd . Therefore A B is not unequal to AC , that is , it is equal to it . Wherefore , if two angles , & c . Q. E. D. COR . Hence ...
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...