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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Seite 15
... equi- lateral triangle DFE , and join F , C , the straight line FC drawn from the given point c shall be at right angles to the given straight line AB . A D C E Because DC is equal to CE , and FC common to the two triangles DCF , ECF ...
... equi- lateral triangle DFE , and join F , C , the straight line FC drawn from the given point c shall be at right angles to the given straight line AB . A D C E Because DC is equal to CE , and FC common to the two triangles DCF , ECF ...
Seite 36
... equi- valent ( 37. 1. ) to the triangle EBC , because they are upon the same base BC , and be- tween the same parallels BC , AE : but the parallelogram ABCD is double ( 34. 1. ) of D the triangle ABC , because the diameter AC divides it ...
... equi- valent ( 37. 1. ) to the triangle EBC , because they are upon the same base BC , and be- tween the same parallels BC , AE : but the parallelogram ABCD is double ( 34. 1. ) of D the triangle ABC , because the diameter AC divides it ...
Seite 37
... equi- valent ( 38. 1. ) to the triangle A EC , since they are upon equal bases BE , EC , and between the same parallels BC , AG ; therefore the triangle ABC is double of the triangle AEC : and the parallelogram FECG is likewise double ...
... equi- valent ( 38. 1. ) to the triangle A EC , since they are upon equal bases BE , EC , and between the same parallels BC , AG ; therefore the triangle ABC is double of the triangle AEC : and the parallelogram FECG is likewise double ...
Seite 39
... equi- valent to the triangle ADB , having the angle HKF equal to the angle E and to the straight line GH apply ( 44. 1. ) the parallelogram GM equivalent to the triangle DBC , having the angle GHM equal to the angle E. Then because the ...
... equi- valent to the triangle ADB , having the angle HKF equal to the angle E and to the straight line GH apply ( 44. 1. ) the parallelogram GM equivalent to the triangle DBC , having the angle GHM equal to the angle E. Then because the ...
Seite 40
... equi- valent to the parallelogram HF , and the triangle DBC to the parallelogram GM ; the whole rectilineal figure ABCD is equivalent to the whole parallelogram KFLM ; therefore the parallelogram KFLM has been described equivalent to ...
... equi- valent to the parallelogram HF , and the triangle DBC to the parallelogram GM ; the whole rectilineal figure ABCD is equivalent to the whole parallelogram KFLM ; therefore the parallelogram KFLM has been described equivalent to ...
Andere Ausgaben - Alle anzeigen
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Keine Leseprobe verfügbar - 2015 |
Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides Keine Leseprobe verfügbar - 2018 |
Elements of Geometry: Consisting of the First Four,and the Sixth, Books of ... Euclides Keine Leseprobe verfügbar - 2013 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 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
Seite 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.
Seite 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.
Seite 9 - If two triangles have two sides of the one equal to two sides of the...