The Elements of Euclid [book 1] for beginners, by J. Lowres1852 |
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Αποτελέσματα 1 - 5 από τα 8.
Σελίδα 14
... triangle are equal , and if the equal sides be produced , the angles below the base ... angle B is common to both ; therefore the two triangles are equal in all ... BAC and BCA are also equal ( Ax . 3. ) , and these are the angles at the ...
... triangle are equal , and if the equal sides be produced , the angles below the base ... angle B is common to both ; therefore the two triangles are equal in all ... BAC and BCA are also equal ( Ax . 3. ) , and these are the angles at the ...
Σελίδα 16
... 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 AC cut off a part A E equal to A D ( Prop . 3. ) : join DE , and upon it describe an equilateral triangle DEF ( Prop . 1 ...
... 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 AC cut off a part A E equal to A D ( Prop . 3. ) : join DE , and upon it describe an equilateral triangle DEF ( Prop . 1 ...
Σελίδα 20
... angle is greater than either of the interior opposite angles . Let the side AB of the triangle ABC be produced to D ... B A C ( Prop . 16. ) ; B C D add to each the angle BCA ; and the angles BAC and BCA are less than the angles BCD and ...
... angle is greater than either of the interior opposite angles . Let the side AB of the triangle ABC be produced to D ... B A C ( Prop . 16. ) ; B C D add to each the angle BCA ; and the angles BAC and BCA are less than the angles BCD and ...
Σελίδα 21
... angle BDC is greater than the interior angle BAC ( Prop . 16. ) , therefore the angle BCD is greater than BAC ; much more then is the angle B C A greater than the angle BA C. Which was to be demonstrated . PROP . XIX . THEOR . If one angle ...
... angle BDC is greater than the interior angle BAC ( Prop . 16. ) , therefore the angle BCD is greater than BAC ; much more then is the angle B C A greater than the angle BA C. Which was to be demonstrated . PROP . XIX . THEOR . If one angle ...
Σελίδα 25
... 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 to D F E , and a ...
... 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 to D F E , and a ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid [Book 1] for Beginners, by J. Lowres Joseph Butler,Thomas Codrington,Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The Elements of Euclid [book 1] for Beginners, by J. Lowres Joseph Butler,Thomas Codrington,Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The Elements of Euclid [book 1] for Beginners, by J. Lowres Joseph Butler,Thomas Codrington,Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 10 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 20 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 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.
Σελίδα 22 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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.