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 12
... PROP . VII . THEOR . UPON the same base , and on the same side of it , there cannot be two triangles having their ... Q. E. D. PROP . VIII . THEOR . If two triangles have 12 EUC . B. L ELEMENTS.
... PROP . VII . THEOR . UPON the same base , and on the same side of it , there cannot be two triangles having their ... Q. E. D. PROP . VIII . THEOR . If two triangles have 12 EUC . B. L ELEMENTS.
Seite 13
... Q. E. D. COR . Hence , and from prop . IV . , it 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 ...
... Q. E. D. COR . Hence , and from prop . IV . , it 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 ...
Seite 18
... Q. E. D. PROP . XV . THEOR . IF two straight lines cut one another , the vertical , or opposite , angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle AEC shall be equal to the angle DEB ...
... Q. E. D. PROP . XV . THEOR . IF two straight lines cut one another , the vertical , or opposite , angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle AEC shall be equal to the angle DEB ...
Seite 19
... Q. E. D. PROP . XVII . THEOR . ANY two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the ...
... Q. E. D. PROP . XVII . THEOR . ANY two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the ...
Seite 20
... Q. E. D. PROP . XVIII . THEOR . THE greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC is also greater than the angle BCA . D ...
... Q. E. D. PROP . XVIII . THEOR . THE greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC is also greater than the angle BCA . D ...
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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
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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...