## Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green1863 |

### Dentro del libro

Resultados 6-10 de 17

Página 9

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**proved**by**proving**separately each of its particular cases : thus , the s , A , B , C , and D are all the s , in a certain figure ABCD ; we**prove**that A is a rt . △ , B a rt . , Ca rt . , and Dart . ; and we say , therefore all the ... Página 10

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**proved**to be , first , equal to the angle BCD , and next , greater than the same angle BCD ; but this is an absurdity . There is little real difference in Geometry between the impossible and the absurd . " ELEMENTS OF GEOMETRY ... Página 20

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**proved**by means of the Axioms . The converse of the 8th Axiom is assumed ; namely , that if the magnitudes are equal , not merely if they are equivalent , they will coincide . 2. The equality spoken of is equality of the sides and of ... Página 21

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**proved**by means of the Axioms . The converse of the 8th Axiom is assumed ; namely , that if the magnitudes are equal , not merely if they are equivalent , they will coincide . 2. The equality spoken of is equality of the sides and of ... Página 22

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**proved**to be equal to and these are the angles below , or on the other side of the base . Wherefore , the angles at the base , & c . COR . - Every equilateral triangle is also equiangular . 14 Rec . E. 11 Нур . 2 Conc . D. 1 by Def . 24 ...### Términos y frases comunes

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

### Pasajes populares

Página 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.

Página 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...

Página 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.

Página 41 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.

Página 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Página 16 - LET it be granted that a straight line may be drawn from any one point to any other point.

Página 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.

Página 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.

Página 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.

Página 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.