## SYLLABUS OF PLANE GEOMETRY |

### Inni boken

Side 1

... drawing and producing straight lines , the Compasses for describing

... drawing and producing straight lines , the Compasses for describing

**circles**and for the transference of distances . ... The construction of an angle**equal**to a given angle ; of an angle**equal**to the sum of two given angles , & c . Side 27

**Circles**that have a common centre are said to be concentric . ... ( c ) The distance of a point from the centre of a**circle**is less than ,**equal**to , or greater than the radius , according as the point is within , on , or without the ... Side 28

In the same circle , or in

In the same circle , or in

**equal circles**, equal arcs subtend equal angles at the centre , and of two unequal arcs the greater subtends the greater angle at the centre . [ By Rule of Conversion . ] COR . Equal sectors of the same ... Side 29

COR . 3. If from any point within a circle more than two straight lines drawn to the circumference are equal , that point is the centre , THEOR . II . In the same circle , or in

COR . 3. If from any point within a circle more than two straight lines drawn to the circumference are equal , that point is the centre , THEOR . II . In the same circle , or in

**equal circles**... Side 49

In the same circle or in

In the same circle or in

**equal circles**angles at the centre and sectors are to one another as the arcs on which they stand . [ In Book III . it was only necessary to consider arcs less than the whole circumference and angles less than ...### Hva folk mener - Skriv en omtale

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according altitude angles are equal angles equal antecedent arcs base bisects Book called centre chord circumference circumscribe common conjugate consequent construct corresponding Definitions denoted describe diameter difference distance divided draw equal angles equal circles externally extremes formed former four GEOMETRY given angle given circle given point given ratio given straight line greater angle Hence identically equal inscribed intercepts interior angles internally intersection kind less Limits Loci locus magnitudes major mean meet minor arcs multiple opposite opposite angles pair parallel parallelogram passes perpendicular point of contact polygon position PROB produced proof proportional proposition quadrilateral radii radius ratio compounded ratios are equal rectangle contained rectilineal figure regular respectively right angles Rule of Conversion sectors segment sides similar square stand straight line drawn subtended Superposition SYLLABUS taken tangent THEOR Theorem third touch triangle true unequal vertex whence whole wholly

### Populære avsnitt

Side 14 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Side 17 - Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles...

Side 14 - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.

Side 13 - Any two sides of a triangle are together greater than the third side.

Side 23 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 13 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

Side 34 - If the distance between the centres of two circles is equal to the difference of their radii, the two circles will touch each other internally.

Side 56 - If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square on the mean ; and conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals.

Side 28 - In the same circle, or in equal circles, equal arcs are subtended by equal chords : and conversely, equal chords subtend equal arcs.

Side 4 - The enunciation of a Theorem consists of two parts, — the hypothesis, or that which is assumed, and the conclusion, or that which is asserted to follow therefrom. Thus in the typical Theorem, If A is B, then C is D, (i), the hypothesis is that A is B, and the conclusion, that C is D.