Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green1863 |
From inside the book
Results 1-5 of 10
Page 5
... Suppose . Superp . Superponen- .do , by superposition . Theor . Theorem . Q.E.D. , quod erat demonstrandum , which was the thing to be proved . Q.E.F. , quod erat faciendum , which was the thing to be done . assum . reduced to an ...
... Suppose . Superp . Superponen- .do , by superposition . Theor . Theorem . Q.E.D. , quod erat demonstrandum , which was the thing to be proved . Q.E.F. , quod erat faciendum , which was the thing to be done . assum . reduced to an ...
Page 24
... with EF , BA and CA shall coincide with ED , FD . For , suppose that BC coincides with EF , but not BA and CA with ED , FD , but with other lines , as EG , FG , → FG ; then on this supp . , in 24 EUCLID'S ELEMENTS .
... with EF , BA and CA shall coincide with ED , FD . For , suppose that BC coincides with EF , but not BA and CA with ED , FD , but with other lines , as EG , FG , → FG ; then on this supp . , in 24 EUCLID'S ELEMENTS .
Page 28
... Suppose that the ang . CBA is equal to ang . ABD ; D. 1 by Def . 10. then each of the angles is a right angle . CASE II . - But suppose that the angle CBA is not equal to angle ABD ; C. 1 by P. 11 . 2 Def . 10 D. 1 by Ax . 8 . 23 4 56 ...
... Suppose that the ang . CBA is equal to ang . ABD ; D. 1 by Def . 10. then each of the angles is a right angle . CASE II . - But suppose that the angle CBA is not equal to angle ABD ; C. 1 by P. 11 . 2 Def . 10 D. 1 by Ax . 8 . 23 4 56 ...
Page 37
... Suppose that BAC is = EDF : 3 Hyp . & P. 4 then base BC : E 4 Hyp . 5 Conc . 6 Sup . 8 Hyp . 9 Conc . B base EF : But BC is EF ; BAC is EDF . Again , suppose BAC < EDF ; base EF : But BC is BAC is EF ; 4 EDF . EDF ; .. BAC is > EDF . 7 ...
... Suppose that BAC is = EDF : 3 Hyp . & P. 4 then base BC : E 4 Hyp . 5 Conc . 6 Sup . 8 Hyp . 9 Conc . B base EF : But BC is EF ; BAC is EDF . Again , suppose BAC < EDF ; base EF : But BC is BAC is EF ; 4 EDF . EDF ; .. BAC is > EDF . 7 ...
Page 39
... Suppose AC to measure 70 feet or yards , ang . A 909 , ang . ACB 669 ; at A make a right angle , and on AC set of 70 equal parts ; at C draw an angle of 669 ; the line CB will cut off B , the distance from A : let the distance from A to ...
... Suppose AC to measure 70 feet or yards , ang . A 909 , ang . ACB 669 ; at A make a right angle , and on AC set of 70 equal parts ; at C draw an angle of 669 ; the line CB will cut off B , the distance from A : let the distance from A to ...
Common terms and phrases
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
Popular passages
Page 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.
Page 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...
Page 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.
Page 41 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.
Page 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 16 - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 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.
Page 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.
Page 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.
Page 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.