The Elements of Euclid [book 1] for beginners, by J. Lowres1852 |
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Αποτελέσματα 6 - 10 από τα 22.
Σελίδα 16
... equal to two sides of the other , and also have their bases equal , the angles opposite the equal bases are equal ... B C to EF , and the base AC equal to the base DF ; then the angle в is equal to the angle E ; and the two triangles are ...
... equal to two sides of the other , and also have their bases equal , the angles opposite the equal bases are equal ... B C to EF , and the base AC equal to the base DF ; then the angle в is equal to the angle E ; and the two triangles are ...
Σελίδα 17
... equal to BC ( Const . ) , the side cp 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 ...
... equal to BC ( Const . ) , the side cp 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 ...
Σελίδα 19
... BC meet the line DB at the point в , and make with it the angles DBA and DBC equal to two right angles ; then AB and BC . form one right line . A B E C For , if AB and вс do not form one right line , let any other line BE form with AB a ...
... BC meet the line DB at the point в , and make with it the angles DBA and DBC equal to two right angles ; then AB and BC . form one right line . A B E C For , if AB and вс do not form one right line , let any other line BE form with AB a ...
Σελίδα 21
... equal to the less BC ( Prop.3 . ) ; join DC . Because the sides BD and BC are equal ( Const . ) , the angles BCD and BDC are eqnal ( Prop.5 . ) ; but the angle BDC is greater than the interior angle BAC ( Prop . 16. ) , therefore the ...
... equal to the less BC ( Prop.3 . ) ; join DC . Because the sides BD and BC are equal ( Const . ) , the angles BCD and BDC are eqnal ( Prop.5 . ) ; but the angle BDC is greater than the interior angle BAC ( Prop . 16. ) , therefore the ...
Σελίδα 22
... equal ( Const . ) ; therefore the angle ADB is greater than DBA , and the angle CDB is greater than DBC , and therefore the sides AB and BC opposite the greater angles , are greater than the sides AD and DC opposite to the less ( Prop ...
... equal ( Const . ) ; therefore the angle ADB is greater than DBA , and the angle CDB is greater than DBC , and therefore the sides AB and BC opposite the greater angles , are greater than the sides AD and DC opposite to the less ( Prop ...
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 C ABCD absurd alternate angles angle BAC angle equal angles ABC angles AGF applied base BC BC is equal bisect Book called centre circle coincide common Const Construction demonstrated describe diagonal divided double draw drawn equal Ax equal bases equal Hyp equal Prop equal sides equal to CD equilateral triangle exterior falls figure GEOMETRY given angle given line given point greater interior angles interior opposite angle join less Let the line lines A B manner meet parallel Prop parallelogram perpendicular PROB Problem produced proposition radii radius rectilineal figure remaining respectively equal right angles right angles Prop right line SCHOL Shilling side AB sides BC square standing Take THEOR theorem triangle ABC vertex W. W. D. PROP whole
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.