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

### Dentro del libro

Resultados 6-10 de 29

Página 8

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**propositions**are proved to be true . Thus , in the 15th Prop . , bk . i . , the assertion is made that " the opposite ...**proposition**in the demonstration of which we need this established truth , we do not again go through all the steps ... Página 9

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**proposition**or inference shall be made . Now , that this may be done , there must be something in common contained in both the**propositions**, with which common thing , as with a test or standard , the other two things are compared : we ... Página 10

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**propositions**in this whole booke , depende of these groundes and principles following , which by reason of their playnnes neede no greater declaration , yet to remoue all ( be it neuer so litle ) obscuritie , there are here set certayne ... Página 17

... from centre B , with BC , describe the CHG ; and from centre D , with DG , describe the GLK ; then the st . line AL , from A , is equal to the given st . line BC . K H D B D.1 by C. 4 , 5 . 2 Def .

... from centre B , with BC , describe the CHG ; and from centre D , with DG , describe the GLK ; then the st . line AL , from A , is equal to the given st . line BC . K H D B D.1 by C. 4 , 5 . 2 Def .

**PROPOSITIONS**. - BOOK I. 17. Página 18

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**proposition**admits of it , the learner's im- provement is much promoted by varying the mode of the solution . He may solve any of the twelve cases for himself . E PROP . 3. - PROB . From the greater of two given st . lines to cut off a ...### 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.