Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green1863 |
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Αποτελέσματα 1 - 5 από τα 9.
Σελίδα 9
... ABCD ; we prove that A is a rt . △ , B a rt . , Ca rt . , and Dart . ; and we say , therefore all the angles of the figure ABCD are right angles . The argument a fortiori , ' by the stronger reason , proves that a given predicate ...
... ABCD ; we prove that A is a rt . △ , B a rt . , Ca rt . , and Dart . ; and we say , therefore all the angles of the figure ABCD are right angles . The argument a fortiori , ' by the stronger reason , proves that a given predicate ...
Σελίδα 47
... ABCD be a 2 Conc . 1 . دو 39 2 . 3 . diameter ; and BC its A then AD , and △ B = / C ; AB CD , and AC = BD ; also A ... ABCD , and the diameter bisects the . 11 Rec . Wherefore , the opposite sides and angles of , & c . SCH . - 1 ...
... ABCD be a 2 Conc . 1 . دو 39 2 . 3 . diameter ; and BC its A then AD , and △ B = / C ; AB CD , and AC = BD ; also A ... ABCD , and the diameter bisects the . 11 Rec . Wherefore , the opposite sides and angles of , & c . SCH . - 1 ...
Σελίδα 48
... ABCD , DBCE , be on the same base BC , 2 . 99 Conc . and between the same s AE and BC ; then the ABCD theDBCE . D. 1 by P. 34. Because 2 Ax . 6 48 EUCLID'S ELEMENTS .
... ABCD , DBCE , be on the same base BC , 2 . 99 Conc . and between the same s AE and BC ; then the ABCD theDBCE . D. 1 by P. 34. Because 2 Ax . 6 48 EUCLID'S ELEMENTS .
Σελίδα 49
... ABCD , DBCE are each double of A DBU , ABCD the DBCE . CASE II . Sup . Let AD and EF be not terminated in one point D. D. 1byH.1 & P.34 . ABCD is a .. AD : BC ; 1 2 H. 1 , & P.34 and EBCF a A DE FAE DF .. EF = BC ; 3 Ax . 1 . and ...
... ABCD , DBCE are each double of A DBU , ABCD the DBCE . CASE II . Sup . Let AD and EF be not terminated in one point D. D. 1byH.1 & P.34 . ABCD is a .. AD : BC ; 1 2 H. 1 , & P.34 and EBCF a A DE FAE DF .. EF = BC ; 3 Ax . 1 . and ...
Σελίδα 50
... ABCD ABCD . EFGH . Also EBCH EFGH ; Therefore , parallelograms upon equal bases , & c . Q.E.D. APP . - 1 . The Diagonal Scale is constructed on the principle of parallelograms on equal bases and between the same parallels being equal ...
... ABCD ABCD . EFGH . Also EBCH EFGH ; Therefore , parallelograms upon equal bases , & c . Q.E.D. APP . - 1 . The Diagonal Scale is constructed on the principle of parallelograms on equal bases and between the same parallels being equal ...
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD adjacent angles altitude angle equal angular point Axiom base BC bisected centre circle circumference coincide CON.-Pst Conc construct Deansgate diagonal diameter divided drawn equal bases equal sides equal triangles equil Euclid exterior angle four rt given line given point given st hypotenuse inference interior angles intersect JOHN HEYWOOD join Let the st line BC line CD measure meet miles opposite angles parallel parallelogram perpendicular Plane Geometry produced PROP proposition proved Quæs rectangle rectil rectilineal angle rectilineal figure right angles Scale of Equal side AC sides and angles square straight line surface Syene Theodolite theorem thing vertex Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 36 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Σελίδα 17 - 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 17 - 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. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
Σελίδα 41 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.
Σελίδα 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 16 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 54 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 21 - If two angles of a triangle be equal to one another, the sides also which subtend, or are opposite to, the equal angles, shall be equal to one another.
Σελίδα 22 - 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.
Σελίδα 12 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.