The Elements of Euclid [book 1] for beginners, by J. Lowres1852 |
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Página 13
... BC and EF must also coincide , if not two right lines would inclose a space , which is impossible ( Ax . 10. ) . Therefore the base BC coincides with EF , and is equal to it ( Ax . 8. ) . And as the sides of the angle B , coincide with ...
... BC and EF must also coincide , if not two right lines would inclose a space , which is impossible ( Ax . 10. ) . Therefore the base BC coincides with EF , and is equal to it ( Ax . 8. ) . And as the sides of the angle B , coincide with ...
Página 14
... base are also equal . Let ABC be an isosceles triangle , having the sides AB and вc equal ; then the angles BAC and ... BC in the one , are equal to the sides G B F A B and BA in the other ( Hyp . ) , and the angle B is common to both ; ...
... base are also equal . Let ABC be an isosceles triangle , having the sides AB and вc equal ; then the angles BAC and ... BC in the one , are equal to the sides G B F A B and BA in the other ( Hyp . ) , and the angle B is common to both ; ...
Página 15
... base , and on the same side of it , have the sides which terminate in one end of the base equal , those sides which ... BC and BD are not equal . CASE 1. When the vertex of each tri- angle is without the other . A B Join CD , and if it be ...
... base , and on the same side of it , have the sides which terminate in one end of the base equal , those sides which ... BC and BD are not equal . CASE 1. When the vertex of each tri- angle is without the other . A B Join CD , and if it be ...
Página 16
... bases equal , the angles opposite the equal bases are equal , and the two triangle . are equal in all respects . Let ABC and DEF be two tri- angles , having the side AB equal to DE , the side B C to EF , and the base AC equal to the base ...
... bases equal , the angles opposite the equal bases are equal , and the two triangle . are equal in all respects . Let ABC and DEF be two tri- angles , having the side AB equal to DE , the side B C to EF , and the base AC equal to the base ...
Página 17
... BC ( Const . ) , the side CD is common to both , and the angle A CD is equal to BCD ( Const . ) ; therefore the base AD is equal to BD ( Prop . 4. ) , and therefore the given line AB is bisected in D. Which was to be done . COR . By ...
... BC ( Const . ) , the side CD is common to both , and the angle A CD is equal to BCD ( Const . ) ; therefore the base AD is equal to BD ( Prop . 4. ) , and therefore the given line AB is bisected in D. Which was to be done . COR . By ...
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.