Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green1863 |
Inni boken
Resultat 1-5 av 9
Side 16
... fall upon and cover all the parts and boundaries of another figure . the two figures are equal . The name of Super- position is given to this process , which when actually performed , is the proof to the senses ; when only conceived of ...
... fall upon and cover all the parts and boundaries of another figure . the two figures are equal . The name of Super- position is given to this process , which when actually performed , is the proof to the senses ; when only conceived of ...
Side 20
... fall on the line DF : But AC being DF , .. the C shall fall on the F ; and B falling on E , and C on F , the line B C falls on the line E F : - · · For if , though B falls on E , and Con F , BCdoes not fall on EF , then two st . lines ...
... fall on the line DF : But AC being DF , .. the C shall fall on the F ; and B falling on E , and C on F , the line B C falls on the line E F : - · · For if , though B falls on E , and Con F , BCdoes not fall on EF , then two st . lines ...
Side 21
... fall on the line DF : = · · But AC being DF , ... the C shall fall on the F ; and B falling on E , and C on F , the line BC falls on the line E F : • · For if , though B falls on E , and C on F , BCdoes not fall on EF , then two st ...
... fall on the line DF : = · · But AC being DF , ... the C shall fall on the F ; and B falling on E , and C on F , the line BC falls on the line E F : • · For if , though B falls on E , and C on F , BCdoes not fall on EF , then two st ...
Side 39
... falling upon two other st . lines makes the alternate angles equal to one another ; these two lines shall be parallel . CON . - Pst . 2.-DEM.-P. 16 , Def . 35 . E. 1 Hyp . 1 . Let the st . line EF fall A 2 2 . " " 3 Conc . on the two st ...
... falling upon two other st . lines makes the alternate angles equal to one another ; these two lines shall be parallel . CON . - Pst . 2.-DEM.-P. 16 , Def . 35 . E. 1 Hyp . 1 . Let the st . line EF fall A 2 2 . " " 3 Conc . on the two st ...
Side 40
... fall on AB , CD , and make the alt . s AFG and FGD equal ; then the lines AB and CD are parallel . At G draw GA | AB ; take GD = AF , & join F , D . In As AGF , DFG , ... GD = AF , GF common , AFG : E A -B F D H and FGD ; AG = DF , GDF ...
... fall on AB , CD , and make the alt . s AFG and FGD equal ; then the lines AB and CD are parallel . At G draw GA | AB ; take GD = AF , & join F , D . In As AGF , DFG , ... GD = AF , GF common , AFG : E A -B F D H and FGD ; AG = DF , GDF ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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...
Side 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.
Side 41 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.
Side 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 16 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 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.
Side 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.
Side 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.
Side 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.