The Elements of Euclid [book 1] for beginners, by J. Lowres1852 |
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Página 12
... remaining part AG is equal to BE ( AX . 3. ) ; but the line BC is also equal to BE , being radii of the same circle CEF : since then each of the lines AG and BC is equal to the same line BE , they are equal to one another ( Ax . 1 ...
... remaining part AG is equal to BE ( AX . 3. ) ; but the line BC is also equal to BE , being radii of the same circle CEF : since then each of the lines AG and BC is equal to the same line BE , they are equal to one another ( Ax . 1 ...
Página 13
... remaining angles of the other , and the two triangles are equal in all respects . Let ABC and DEF be two triangles , having the side A B equal to DE , the side AC equal to DF , and the angle a equal to the angle D ; then the base B C is ...
... remaining angles of the other , and the two triangles are equal in all respects . Let ABC and DEF be two triangles , having the side A B equal to DE , the side AC equal to DF , and the angle a equal to the angle D ; then the base B C is ...
Página 16
... remaining sides of the one equal to the remaining sides of the other . PROP . IX . PROB . To bisect a given rectilineal angle . Let BAC be the given angle , it is required to bisect it . D E Take any point D in the side a B , and from ...
... remaining sides of the one equal to the remaining sides of the other . PROP . IX . PROB . To bisect a given rectilineal angle . Let BAC be the given angle , it is required to bisect it . D E Take any point D in the side a B , and from ...
Página 19
... remaining angles DBE and DBC are equal ( Ax . 3. ) , a part equal to the whole which is absurd ; therefore BE does not form a right line with AB ; and in the same manner it can be proved that no other line but BC can form a right line ...
... remaining angles DBE and DBC are equal ( Ax . 3. ) , a part equal to the whole which is absurd ; therefore BE does not form a right line with AB ; and in the same manner it can be proved that no other line but BC can form a right line ...
Página 25
... remaining sides and angle in the one , are respectively equal to the remaining sides and angle in the other , and the two triangles are also equal . In the triangles A B C and D E F , let the angle BAC be equal to EDF , the angle A C B ...
... remaining sides and angle in the one , are respectively equal to the remaining sides and angle in the other , and the two triangles are also equal . In the triangles A B C and D E F , let the angle BAC be equal to EDF , the angle A C B ...
Otras ediciones - Ver todas
The Elements of Euclid [Book 1] for Beginners, by J. Lowres Joseph Butler,Thomas Codrington,Euclides Sin vista previa disponible - 2018 |
The Elements of Euclid [book 1] for Beginners, by J. Lowres Joseph Butler,Thomas Codrington,Euclides Sin vista previa disponible - 2018 |
The Elements of Euclid [book 1] for Beginners, by J. Lowres Joseph Butler,Thomas Codrington,Euclides Sin vista previa disponible - 2018 |
Términos y frases comunes
A B and C D A B is equal ABC and ABD ABCD adjacent angles alternate angles angle ABC angle BAC angle equal angle opposite angles AGF angles CAB angles DBA base BC BC is equal BD Prop BGF and EHD bisect coincide DBC are equal demonstrated describe an equilateral diagonal draw EHD are equal equal Ax equal bases equal Hyp equal Prop equal sides equal to CD equal triangles equilateral triangle EUCLID's ELEMENTS exterior given angle given line given point greater than AC hypotenuse interior angles interior opposite angle isosceles triangle join Let the line line BC lines A B parallel Prop parallel to BC parallelogram perpendicular price One Shilling PROB produced proposition rectilineal figure respectively equal right angles Prop SCHOL side A B sides AB sides BC THEOR triangle ABC triangles are equal Twickenham vertex W. W. D. PROP
Pasajes populares
Página 10 - Things which are halves of the same are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Página 10 - Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another.
Página 40 - 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 sides.
Página 10 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Página 10 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 39 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Página 20 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 29 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Página 22 - Any two sides of a triangle are together greater than the third side.
Página 10 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal.